Turnbull's comments came after Saturday's general election failed to produce a clear winner and raised the prospect of a hung parliament.
Turnbull's conservative coalition secured 70 seats, opposition Labor 67, with 80 per cent of the vote counted. Eight seats are still in doubt, according to Australian Broadcasting Corporation. The major parties need 76 seats to form a majority government.
Vote counting is expected to drag on for days, possibly weeks, leaving Australia in a political vacuum.
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.
"There are lessons to be learnt from this election," he said.
Turnbull said more than three million votes would be added to the count in coming days and while he remained confident of securing a majority, he accepted responsibility for the Coalition's low vote.
"The Australian people have voted and we respect the result."
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," Brandis said.
After the election, crossbench and independent MPs have emerged as kingmakers. Turnbull and Shorten on Sunday started negotiations with them.
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.
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