Malcolm Turnbull and Bill Shorten have begun reaching out to crossbench MPs, as the prime minister remained hopeful of returning with a slim majority.
On current counting the Liberal-Nationals coalition holds 72 seats to Labor's 67, with four independents and one Green on the crossbench.
But six seats remain in doubt: Chisholm, Forde, Herbert, Hindmarsh where Labor leads, and Dunkley and Gilmore where the coalition is ahead.
The prime minister put the number of undecided seats at 12, with recounts likely in a number of other close battles.
"I remain quietly confident that a majority coalition government will be returned," Mr Turnbull told reporters in Sydney on Sunday.
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Coalition strategists believe postal and pre-poll votes will favour the government.
Mr Turnbull promised the new parliament, which could sit in early August, would be resolved "without division or rancour".
"What we will do is ensure that we work constructively and effectively with all of the members of the new parliament to ensure that we deliver the stability and the leadership that Australians expect," he said.
Mr Turnbull and Mr Shorten both have spoken with a number of crossbenchers.
The Labor leader said he wanted to play a "constructive" role in the new parliament and deliver on jobs, health, education and climate change.
Tasmanian independent MP Andrew Wilkie said the prime minister had phoned him on Sunday morning.
But the MP added he would not do any deals with either major party and would support all motions and bills solely on their merits.
Nick Xenophon, whose team is set to win one lower house seat and three senators in South Australia, said he would sit down in good faith with the major parties.
But his initial talks will be with whichever party has the most MPs.
Indi MP Cathy McGowan, who has also been contacted by Mr Turnbull, says she has a "good working relationship" with the prime minister and had agreed to stay in contact in coming days.
A Labor loss will automatically trigger a leadership spill and a ballot of grassroots and caucus members, as occurred for the first time in 2013.
Mr Shorten, who hails from Labor's Right faction, was upbeat about his future.
"I have never been more certain of my leadership as I am this morning," he said.
A number of Left faction heavyweights are backing Mr Shorten over the Left's Anthony Albanese, who lost the leadership ballot in 2013 despite winning a majority of grassroots votes.
The Australian Electoral Commission must wait for 13 days for the final postal votes to come in, which could make a difference in some seats.
"We will see a lot of movement in those seats over a couple of days," commissioner Tom Rogers said.
Minor parties and independents were the big winners in the election taking 23 per cent of the vote.
In the Senate, a new cohort of crossbenchers is expected to take up seats, including Derryn Hinch, Pauline Hanson, and two of Nick Xenophon's running mates.
They'll likely join returned independents Senator Xenophon and Jacqui Lambie, with the Greens on track to take eight or nine seats, down one or two on their previous result.
The new Senate electoral system proved difficult for more than 530,000 voters who cast informal ballots.
