The High Court will determine whether Joyce, former Greens senators Larissa Waters and Scott Ludlam, One Nation senator Malcolm Roberts and former minister Matt Canavan are eligible to sit in Parliament under section 44 of the constitution due to their dual citizenship.
Senators Waters and Ludlam have already resigned from Parliament and Senator Canavan has stood aside from the Cabinet pending the court outcome.
Joyce, who was born in Tamworth, New South Wales, revealed in Parliament on Monday he had been advised by the New Zealand High Commission that he could be a New Zealander via his father who was born in New Zealand but left in 1947.
Turnbull told Parliament Joyce was qualified to sit in Parliament and the High Court would find in favour of him.
Attorney-General George Brandis doesn't share his Prime Minister's absolute confidence though.
"You can never be absolutely certain of outcomes in the High Court," he told ABC radio yesterday, noting none of the seven judges on the bench sat on earlier cases that considered Section 44 of the constitution.
"We're reasonably confident he doesn't have a problem here."
Labor, meanwhile, accused the Prime Minister of trying to influence the judges and ignore the separation of powers that exists between Government and the courts.
"These were the comments of an arrogant Prime Minister who came perilously close to directing the High Court," shadow attorney-general Mark Dreyfus told ABC radio.
Brandis hit back that Turnbull was not telling the court what to rule.
"It is not a directive at all," he said.
Joyce has now renounced his New Zealand citizenship.
The coalition accuses Labor leader Bill Shorten of treachery and international conspiracy for tipping off the New Zealand Government about the Joyce's potential citizen status.
An Australian Labor Party staffer suggested to New Zealand Labour Chris Hipkins that he might like to ask Internal Affairs Minister Peter Dunne whether a child born in Australia to a New Zealand father automatically had New Zealand citizenship - which he subsequently did. There was no specific reference in the question to Joyce, nor was Hipkins aware of any issue relating to Joyce.
Dunne said any suggestion Hipkins instigated the issue was "utter nonsense". "They were not the instigator. Australian media inquiries were," Dunne tweeted.
But that did not stop Turnbull and Bishop ramping up their attack on Shorten.
"He chose to plot with his Labour Party comrades across the ditch," Turnbull told Parliament.
Shorten told caucus colleagues the Government was engaging in conspiracy theories.
"The Turnbull Government is in a constitutional crisis caused by its own negligence," Shorten said. "The Deputy Prime Minister, who I suppose we should now call the Foreign Minister or the leader of the dual Nationals, is unwittingly or not a dual citizen."