The meeting came a day after an extraordinary press conference in Canberra, at which the Deputy Prime Minister condemned the Prime Minister for making hurtful and "inept" comments about Mr Joyce's affair with his former media adviser, who is pregnant with his child.
Veterans Affairs Minister Michael McCormack - considered the most likely National lawmaker to replace Joyce - did not rule out a leadership challenge yesterday but said he didn't want to get "too far ahead of myself", the Sun-Herald reported. He also criticised Mr Turnbull's changes to the ministerial code of conduct banning sexual relations between ministers and their staff.
AAP understands the pressure has only made some Nationals stand even more firmly behind Mr Joyce.
Malcolm Turnbull isn't about to tell the United States what to do about its gun deaths but says Australia has a lot to thank John Howard for regarding the gun controls he put in place in the 1990s.
Despite Mr Turnbull's apparent belief that his deputy would resign, Mr Joyce, leader of the rural-based National Party, hit back and accused the Prime Minister of worsening his family's turmoil.
'The real issue is the bad hurt and humiliation that Barnaby, by his conduct, has visited on his wife, Natalie and their daughters and indeed, his new partner, ' Mr Turnbull said in Canberra.
Nationals MPs toldThe Australian Mr Joyce's position was "untenable" and demanded he step down before the next party room meeting on Monday or face a leadership spill, after a public war of words with the Prime Minister.
Frank Reich's Colts' coaching staff taking shape
Indianapolis Colts quarterback Andrew Luck (12) drops back to pass against the Jacksonville Jaguars at Lucas Oil Stadium. Indianapolis Colts quarterback Andrew Luck is ready to get started with the team's new head coach, Frank Reich .
Turnbull's predecessor, former Prime Minister Tony Abbott, said yesterday that if politicians wanted to give each other advice, they should do so by knocking on their door and picking up the phone to talk directly.
"Everyone is expendable", Mr Howarth said. Earlier on Saturday, Liberal senator Ian Macdonald called for Mr Joyce to be demoted to the backbench on account of his actions.
"This government is in crisis", said Bill Shorten, leader of the main opposition Labor Party.
"Obviously what else transpires - not just in our electorates but obviously on a national front - has to be thought through", he told Fairfax. "There's a massive question to answer". He also asked Joyce to "consider his position". "That's code for saying, I need you to resign".
Ms Campion is due to have the 50-year-old's baby in April. "He has done such an wonderful job for us throughout his leadership that he has earned the opportunity to see this through", he said.
Serious question marks remained around conflicts of interest, the soliciting of gifts and misuse of public funds. "Internationally it makes Australia a laughing-stock", Senator Di Natale said.
"Does he care more about himself or the country?"