Counting of 1.5 million postal and absentee votes, critical for election, began this morning.
Initial vote counts were inconclusive. Turnbull's conservative coalition secured 68 seats, opposition Labor 67, with 10 seats in doubt, according to Australian Broadcasting Corporation. The major parties need 76 seats to form a majority government.
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Labor leader Bill Shorten yesterday asked Turnbull to go, saying, "Mr Turnbull clearly doesn't know what he is doing. Quite frankly, I think he should quit."
But Turnbull rejected his demand.
"He would say that, wouldn't he?" Turnbull reporters.
"He obviously couldn't think of anything else better to say," Turnbull said.
He also acknowledged the massive swing against the Coalition and the "disillusionment" of voters towards the major political parties after Saturday's election.
"There are lessons to be learnt from this election," he said.
He vowed to "look to how we are going to address those concerns".
Attorney-General George Brandis said the Coalition remained "quietly confident" it could secure a "working majority" in the Lower House.
"We hope that a final result in the narrowly contested seats will be available in coming days," Senator Brandis said.
But Deputy Prime Minister Barnaby Joyce said if that was not the case he expected the regional independents to side with the Coalition.
After the election, crossbench and independent MPs have emerged as kingmakers. Turnbull and Shorten on Sunday started negotiations with them.
Senator Nick Xenophon, who is positioning himself as the new parliamentary kingmaker, has signalled that he is prepared to enter some form of minority government agreement with either Turnbull or Shorten.
Australia has had five prime ministers in the past six years. Turnbull became prime minister in September after ousting his colleague Tony Abbott in a party room vote.
Meanwhile, Pauline Hanson, founder of the controversial far right One Nation party, said it was "absolutely fantastic" that she would be returning to politics after eight failed attempts, and believed her party may claim at least five other Senate spots nationally.
Hanson wants to abolish the Racial Discrimination Act and wants a referendum on changing the part of the constitution that protects the free practice of religion.
"They feel that they have been swamped by Asians," the leader said, adding"And regardless of that now, a lot of Australians feel Asians are buying up prime agricultural land, housing".
She said she was not in favour of returning to a White Australia policy, but a return to the old-fashioned values that made the nation great.
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