Independent MP Kerryn Phelps has maintained her lead as counting continues in the Sydney seat of Wentworth.
The latest Australian Electoral Commission figures published at 1pm on Monday show Dr Phelps on 51.14 per cent of the two-candidate preferred vote with a lead of 1676 votes.
Still to be counted were 1456 declaration votes, including postal and provisional ballots.
Dr Phelps, whose vote will be crucial in the minority parliament, said she had yet to have a conversation with Prime Minister Scott Morrison but had received a text message from him saying "counting was still going on".
"Certainly I would be wanting to have a conversation with the prime minister," she told Sky News.
"The first order of business is to get kids off Nauru."
She said asylum-seeker children needed urgent medical attention in Australia.
Then an independent body should be set up to assess their resettlement options.
Asked whether Home Affairs Minister Peter Dutton should be referred to the High Court over his childcare interests, she said: "We need to be very rigorous and inquiring about any legislation or motions or referrals and make sure the right decisions are made."
Senior Liberals are licking their wounds from the likely by-election defeat.
Cabinet minister Simon Birmingham said it was up to his party to quell the profound fury of the electorate with strong communication about the government's policy achievements.
He said the coalition paid the price for dumping Malcolm Turnbull as prime minister, which triggered his resignation from Wentworth.
Nationals frontbencher Darren Chester said the people of Wentworth had sent a message after losing their popular local member.
"I think once you hand the voters a baseball bat, you can hardly be surprised if they use it," Mr Chester told the ABC.
A win for Dr Phelps will leave the House of Representatives with six crossbenchers, 75 coalition MP sand 69 Labor MPs.
Three crossbenchers, Cathy McGowan, Rebekha Sharkie and Bob Katter, want the government to run its full term.
Independent Mr Wilkie will not guarantee confidence, while Greens MP Mr Bandt said an election had to be called because "the sooner we turf out this rotten government, the better".
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