"I promise the Australian people, we will continue the work of putting together a policy agenda for the next national Labor government, a program which will re-win the confidence and the support of working class and middle-class Australians," he said.
The Centre Alliance MP Rebekha Sharkie held out a challenge from Liberal Georgina Downer, owing her victory in the seat of Mayo to “people power”.
10.20pm: Labor's Patrick Gorman claims victory in Perth
"Let's finish the job at the next general election whenever Turnbull has the guts to call it," Mr Gorman told supporters in WA.
Meanwhile, in Fremantle, Labor's Josh Wilson comfortably retained his seat.
10.02pm: Super Saturday results
Braddon: ALP retains 52.2 per cent
Longman: ALP retains 54.99 per cent
Mayo: Centre Alliance retains 58.4 per cent
Fremantle: ALP retains 66.8 per cent
Perth: ALP retains 61.4 per cent
Source: AEC; figures as at 10pm
9.40pm: Labor's Justine Keay re-elected to Braddon seat after disqualification
Justine Keay has held on to the marginal Tasmanian electorate of Braddon.
“I will fight for you today, I will fight for you tomorrow, and I’ll fight for you as long as you will have me," she said, adding: "... And I will take this fight to the next general election."
9.37pm: Alexander Downer sticks by daughter in SA
9.35pm: Liberals don't quite concede in Braddon
Liberal candidate Brett Whiteley spoke to supporters at an event in Braddon, where Labor's Justine Keay is predicted to win. But he didn't concede.
9.20pm: 'Referendum on leadership'
9.16pm: 'What a super Saturday'
Bill Shorten is addressing supporters in Longman alongside Susan Lamb, who reclaimed the seat.
"What a great night for the Labor party, what a great night for women, what a super Saturday," he said.
"They’ve thrown everything at us these last 10 weeks... but we’ve come out of it, I think, in pretty good shape. We should celebrate tonight and tomorrow too.”
"Four from four," he said to applause.
Lamb then stepped in, saying: "The people of Longman have sent a powerful message to Malcolm Turnbull."
"You know, I really love it here. I love the beaches of Bribie. I love the leafy suburbs of Narangba. But most of all I love the people," she said.
"After tonight's result, I will be very proud once again to represent all of you in Federal Parliament. From the bottom of my heart, I want to thank each and every single one of you that are here tonight."
She also thanked Liberal National Party candidate Trevor Ruthenberg for a "clean contest".
9.08pm: Trevor Ruthenberg concedes in Longman
Liberal National Party candidate Trevor Ruthenberg has conceded defeat to Labor's Susan Lamb in the Queensland seat of Longman.
“Thank you, that was a warm welcome, I think I’ll remember that one for a while,” he told supporters.
“This is a strange election in that while I have lost, the community will still benefit from the commitments I have been able to secure from the prime minister and his team of ministers and for that, I will be forever grateful."
He said he "takes responsibility for this result" and said he had a "terrific team".
"Big Trev" was embroiled in controversy earlier this month, apologising to voters after he incorrectly claimed to have a medal for distinguished service in peacekeeping and non-war operations.
9.02pm: Susan Lamb set to regain Longman
Labor's Susan Lamb is set to regain her seat as Federal MP in the marginal Queensland electorate of Longman, despite a challenge from the Liberal-National Party's Trevor Ruthenberg.
Ms Lamb was one of four opposition MPs to quit on the same day after the High Court ruled on ACT Senator Katy Gallagher.
8.40pm: Sharkie delivers victory speech
Sharkie has delivered her victory speech, telling supporters she was "crushed" on the day she resigned, but today, victory was "sweet".
“It has been a marathon of a campaign, but we did this tonight, we did it, because of you,” she told the room.
Sharkie announced she was quitting parliament earlier this year after the High Court ruled Labor senator Katy Gallagher, who didn't renounce her British citizenship in time, was ineligible to sit.
8.34pm: Rebekha Sharkie wins Mayo
Centre Alliance candidate Rebekha Sharkie has secured the South Australian seat of Mayo with a 9.3 per cent swing.
Liberal candidate Georgina Downer has delivered a concession speech, saying she "absolutely respects" the decision of voters.
"I have just spoken to Rebekha Sharkie and have congratulated her on being re-elected. ... She put up an extremely strong fight and I do applaud her," Ms Downer said.
8.12pm: Meanwhile in Braddon ...
8.05pm: Labor's Susan Lamb likely to win Longman
7.47pm: 'It's looking pretty good'
7.30pm: Rebekha Sharkie on track to win Mayo
Centre Alliance candidate Rebekha Sharkie looks likely to secure the South Australian seat.
She was up against Georgina Downer, daughter of former foreign affairs minister Alexander Downer, who campaigned for the Liberal Party.
7.15pm: Early counting shows Labor swing in Braddon
7.11pm: Labor supporters in Longman celebrate early booth results
7.05pm: 'Polling places are now closed'
6.50pm: Labor on track to hold Braddon
Labor appeared on track to hold the Tasmanian seat of Braddon on preferences after a strong early showing from an independent candidate.
AEC figures for Braddon posted at 6.45pm AEST showed swings against Labor and the Liberals of five per cent, with a 17 per cent swing to independent Craig Garland, whose preferences will flow strongly to Labor's Justine Keay.
Polls have also closed in the Queensland seat of Longman and South Australia's Mayo.
Early figures showed a four per cent swing to Labor's Susan Lamb in Longman and seven-point swing against the LNP's Trevor Ruthenberg, as well as a 10 per cent swing to One Nation.
6pm: Counting begins
Counting has begun in Tasmania's Braddon and Queensland's Longman, with the latest Newspoll showing Labor ahead 51-49 in two-party terms in both seats.
The two by-elections were triggered by the resignation of Labor MPs Justine Keay and Susan Lamb over their dual citizenship, with both members re-contesting and facing tough Liberal candidates.
The by-elections in WA's Fremantle and South Australia's Mayo were also triggered by the citizenship fiasco, while former Perth Labor MP Tim Hammond's resignation for family reasons caused the fifth poll - the highest number of by-elections on a single day in Australia's history.
Perth is expected to be won by former WA Labor secretary and Kevin Rudd staffer Patrick Gorman.
5.31: Polls close at 6pm
4.42pm: Shorten in Longman with Susan Lamb
4.11pm: Shorten in Caboolture
Bill Shorten has arrived at Caboolture State High School, with video showing him flanked by several supporters in Labor shirts chanting “Bill! Bill! Bill!”
4.05pm: Slow but steady at Perth polls
Perth's polling booths are seeing a slow but steady stream of voters coming through as the weather warms up.
Inner Perth voters in Highgate seemed more interested in what cake and coffee options were on the table rather than how to vote cards.
3.10pm: Labor's Perth candidate takes swipe at AEC
Labor's candidate for the federal seat of Perth has accused the Australian Electoral Commission of not doing enough to raise awareness of the by-election among voters, AAP reports.
Patrick Gorman, a former Kevin Rudd staffer and state secretary who masterminded Labor's victorious 2017 WA election campaign, says the AEC should have put out their advertisements earlier rather than "just the last few days". He says he'll have an "adult conversation" with them about their efforts.
"I was at a booth over in North Perth today where someone said they hadn't received anything in their letterbox from the Electoral Commission, so obviously they need to look at their distribution," Mr Gorman told reporters on Saturday. "I think they could do more in online communications."
Pre-polling pointed to a low voter turnout for Perth and also Fremantle, which Labor's Josh Wilson is expected to easily win back after being forced to resign over his dual citizenship.
When the two candidates voted at primary school polling booths in their electorates, there were more party officials than voters.
2.45pm: Labor posters depict the Liberals as 'missing' in WA
1.42pm: 'Nice of him to turn up'
There was no time for pleasantries when Malcolm Turnbull and Labor Braddon candidate Justine Keay met at the same primary school polling booth in the knife-edge Tasmanian seat.
Voters at Nixon St School in Devonport were unexpectedly confronted by the prime minister, Bill Shorten and both candidates.
The government hopes to regain the seat in the state's northwest - one it lost to Ms Keay at the 2016 election.
The PM briefly appeared alongside Liberal candidate Brett Whiteley before the pair left for nearby Ulverstone.
"It was nice of him to turn up," Ms Keay said, criticising Mr Turnbull for coming in for "fleeting visits" when it suited.
"It was actually the first time I've actually shook hands with the prime minister but I had to go to him to do it."
1.03pm: Democracy sausage anyone?
It's lunchtime on Super Saturday and the democracy sausages are being served. Speaking (eating) in Braddon, Opposition leader Bill Shorten took a swipe at the PM: "If I was Malcolm Turnbull I'd have to ask for a knife and fork, wouldn't I?"
12.27pm: 'Big Trev' heckled over medal scandal
Home Affairs Minister Peter Dutton and Longman LNP candidate Trevor Ruthenberg have been heckled in the electorate over 'Big Trev's' recent minor scandal around military medals.
Mr Ruthenberg said he didn't think the fuss over his military medal would affect the vote because he had owned up to the error.
He had incorrectly claimed to have won a medal that he was never awarded.
"The community has accepted that apology. It would be nice if Susan Lamb stuck her hand up and accepted the fact we are even here today because she lied to the parliament."
"I think it's going to be some time till we see a result. It's that tight," he said while handing out how-to-vote cards alongside Dutton.
11.26am: Wilson votes
It's a bit of a voter ghost town in Fremantle right now. Labor's Josh Wilson has cast his vote. The dual-citizenship casualty is considered likely to win the race for Freo today.
11.08am: Lamb votes
Labor's Susan Lamb has won over at least one new voter in Longman - her 18-year-old son George. The pair cast their votes at Dakabin State High School in the seat north of Brisbane on Saturday morning.
Lamb is in a tight race for Longman with former state Newman government MP Trevor "Big Trev" Ruthenberg. Mr Ruthernberg won't be able to vote for himself as he lives outside the electorate.
10.28am: Bananas in Pyjamas appear in Mayo
10am: Turnbull gets icy reception in Braddon
Malcolm Turnbull has had a string of awkward run-ins with voters during his by-election campaign appearances. Here's another one filmed in Braddon this morning - UPDATE (11.18am): It's believed the man in the footage is a former greens candidate.
It follows yesterday's run-in on Bribie Island where the PM was heckled by dissatisfied voters who challenged him on penalty rate cuts.
9.33am: Sharkie votes
Centre Alliance candidate Rebekah Sharkie has cast her vote at the Mount Torrens polling booth in Adelaide Hills. She appears to be the first candidate to cast her vote on Super Saturday. Sharkie is tipped to win the seat of Mayo after she was caught in the dual-citizenship saga and was forced to resign.
8.38am: Sharkie and Downer go head to head in Mayo
Centre Alliance MP-turned-candidate Rebekha Sharkie leads Liberal candidate Georgina Downer in Mayo, but neither is giving weight to poll results.
Voters in the former-blue ribbon seat will have the chance to return the electorate to the Liberal fold at Saturday's by-election.
But candidate Georgina Downer would need to discredit consecutive polls to take the seat from Centre Alliance MP-turned-candidate Rebekha Sharkie.
The by-election was triggered after Ms Sharkie - who won Mayo for the Nick Xenophon Team in 2016 - became caught up in the dual citizenship saga and was forced to resign.
She was the first non-Liberal to hold the seat since its 1984 creation and is hoping to repeat the result.
Her opponent, Ms Downer, is the daughter of Howard government foreign minister Alexander, who held the seat for the Liberal Party for 24 years.
A recent poll in The Advertiser put her ahead 59-41 on a two-party basis while a ReachTEL poll of more than 700 voters returned a similar result on Wednesday night.
Counting will start after polling closes at 6pm local time.
8am: Polls open, Longman in for tight fight
Voting is underway in one of Super Saturday's most crucial seat of Longman, north of Brisbane.
Labor's Susan Lamb, whose dual citizenship issues forced the by-election, is in a tight fight with former state Newman government MP Trevor "Big Trev" Ruthenberg.
According to the Newspoll, Ms Lamb leads Mr Ruthenberg 51-49 on a two-party preferred basis.
That's the reverse of other polls this week that had Mr Ruthenberg slightly ahead of Ms Lamb around 51-49.
Before Ms Lamb was forced out of parliament, she held the seat on a razor-thin margin of 0.8 per cent.
Malcolm Turnbull visited Longman on Friday to shore up support for Mr Ruthenberg and took a potshot at Mr Shorten for not visiting the electorate as well.
But some of his momentum was drained after he was taken to task by a pub patron during a seemingly friendly meet-and-greet, which led to several patrons heckling the prime minister.
6.45am: PM and Opposition in Braddon to woo voters
Prime Minister Malcolm Turnbull and Labor leader Bill Shorten know there is more at stake in the knife-edge Braddon by-election than just the result.
Apart from deciding the electorate's next MP, the by-election is being billed as a test of Mr Turnbull's and Mr Shorten's popularity.
Both have made many trips to Tasmania's northwest trying to woo voters and will again be there alongside their candidates on polling day.
Labor has campaigned heavily on improving health, while the Liberals say only they can create jobs and boost business in the region.
Preferences from independent and outspoken fisherman Craig Garland and the Greens could push Labor across the line.
A victory would be historic for the Liberals - a government hasn't won an opposition seat at a by-election for 98 years.
6.25am: Shorten tipped to win Longman, Braddon: Poll
Labor leader Bill Shorten looks set to secure narrow victories in the Longman and Braddon byelections, according to a new poll published in The Australian.
With Mr Shorten's leadership hanging on Saturday's by-elections, minor-party preferences are set to decide tight contests in both seats, but the poll also suggests Labor would have recorded thumping wins in both seats if Anthony Albanese were the federal Labor leader.
The poll shows Labor ahead on a two-party-preferred count of 51 per cent to 49 per cent in the outer metropolitan Queensland seat of Longman and by the same margin in the Tasmanian seat of Braddon.
The poll also indicated the Coalition could still produce an upset win in Longman but it would require the Liberal National Party (LNP) to secure about 80 per cent of One Nation preferences, which would be unlikely.
6am: West Australians urged to vote
West Australians in Perth and Fremantle are encouraged to cast their vote today amid concern turnout could plunge to a record low.
In the first 10 days of pre-polling, early votes for Perth were down 41 per cent on the same time during the 2016 federal election.
In Fremantle, 3200 early votes were cast by Saturday, down 35 per cent compared to the general poll just over two years ago.
A record 15 candidates are contesting Perth.
But with the Liberals not even bothering to contest the federal seats, publicity surrounding the campaigns has been thin.
The Perth by-election is the only one of the five Super Saturday polls not being held because of the dual citizenship fiasco.
Perth has previously been held by major Labor names including Stephen Smith and Alannah MacTiernan, while even bigger party greats such as Kim Beazley senior and former prime minster John Curtin held Fremantle.
For more live updates, follow SBS News reporters on Twitter: Rhiannon Elston in Mayo, Stefan Armbruster in Longman, Brett Mason and James-Elton Pym in Canberra, Myles Morgan and Kyle Brown in Fremantle and Perth, and Marija Zivic in Braddon.
Follow live coverage of Super Saturday on the SBS News website and the SBS News app on iOS and Android.