On Monday evening, opposition Labour Party Leader Bill Shorten called for Turnbull to quit as leader of the Liberal National Party coalition, claiming that the premier was "out of touch" and was unable to provide parliamentary "stability" which he promised to Australian voters throughout his campaign, Xinhua news agency reported.
But on Tuesday, Turnbull said he would not be stepping down from the position and described the Labour leader's attack as purely political.
"Well, he would say that, wouldn't he?" Turnbull said of Shorten, "I'm sure he would (like me to resign)."
"I don't think we'll be taking advice from the leader of the opposition, I think he couldn't think of anything else better to say."
The election's vote count resumed early Tuesday with postal votes and pre-poll votes set to be tallied, two days after the Australian Electoral Commission (AEC) said it could take weeks to get a decisive result from all seats.
Turnbull said he was confident of a forming a majority government despite numerous election analysts suggesting Labor had, by Tuesday, secured more seats than the coalition.
"The count is continuing and we remain confident that we will secure enough seats to have a majority in the parliament," Turnbull told the press.
"All the votes have been cast and it's now simply a matter to count them so we're just awaiting that."
Meanwhile the nation's Attorney General George Brandis has played down concerns that the deadlocked election was bad news for Australia or the coalition; he told the Australian Broadcasting Corporation (ABC) that there's "no such thing as a failed election".
He said there was nothing unusual about the deadlock, despite Trunbull facing a wall of conservative criticism, both from political commentators and from within the far-right factions of his party.
"An election always produces the parliament the people choose," Brandis said.
"Sometimes that's a large majority, sometimes a narrow one, and sometimes the party that forms government relies on other elements of the parliament to govern, but there's nothing unusual here."
Conservative factions of the coalition have already hinted at discontent within the party; the ABC reported that anonymous sources would have no issue ousting Turnbull at a partyroom meeting if he "sells out" the conservative principles of the party while brokering a deal with independent MPs.
A decisive result to determine the government still might not be known for days, while the final results from tightly-contested seats may be in limbo for weeks.