A secret WhatsApp group was set up by a group of National Party MPs to try and bring down Barnaby Joyce.

The Sunday Telegraph reports that support for the embattled Deputy Prime Minister dropped after news of Mr Joyce's affair with staffer Vikki Campion broke.

That was when the secret WhatsApp group of National MPs was set up to look at ways to oust Mr Joyce, reports News.com.au.

Another WhatsApp group that included all National MPs, however, showed support for the Deputy PM.

Nationals MPs told The Australian Mr Joyce's position was "untenable" and demanded he steps down before the next party room meeting on Monday or face a leadership spill, after a public war of words with the Prime Minister.

The news about the secret push to oust Mr Joyce — who is now on a week of leave — comes after Malcolm Turnbull met with his deputy in an effort quell a brewing coalition crisis.

The pair met at the Commonwealth Parliament Offices in Sydney for over an hour on Saturday, where the two leaders discussed their public spat regarding Mr Joyce's affair with a former staffer.

On Thursday, Mr Turnbull described Mr Joyce's affair with former media adviser Ms Campion as a "shocking error of judgment" causing "a world of woe".

That provoked an angry response from Mr Joyce on Friday, who said the prime minister's remarks were "inept" and "unnecessary".

Former prime minister Tony Abbott also waded into the public stoush to take a veiled swipe at Malcolm Turnbull.

"The general rule I always observed was that one party doesn't give another party public advice," Mr Abbott told reporters in Melbourne.

"If a member of parliament has something to say to another member of parliament he or she should knock on the door or pick up the phone." He also criticised Mr Turnbull's changes to the ministerial code of conduct banning sexual relations between ministers and their staff.

"There was a perfectly good code of conduct in place," Mr Abbott said. Earlier on Saturday, Liberal senator Ian Macdonald called for Mr Joyce to be demoted to the backbench on account of his actions.

"Barnaby would have known it would derail the government's line, the government's focus and it really is giving Bill Shorten a free kick," Senator Macdonald told the ABC.

"Clearly, his path is that he's got to take a very, very low profile, I hope on the backbench for, you know, a few months." "It's just got to end," he later told Fairfax media.

Labor MP Pat Conroy described the entire scenario as a "soap opera". "It's a valiant defence of the indefensible," he told ABC News. "There's a massive question to answer.

Malcolm Turnbull said on Thursday that Barnaby needed to consider this position. That's code for saying, I need you to resign."

However, hope remained for Mr Joyce with Nationals MP Michelle Landry telling The Australian that the Nationals leader had the support of the party room — "at this stage".

"He is having a week off and then we'll have our party room meeting Monday after next and we will see," she said.

But the bottom line, according to Greens leader Richard Di Natale, was that Mr Joyce has put self-interest above the national interest.

Serious question marks remained around conflicts of interest, the soliciting of gifts and misuse of public funds.

"And now we have the stability of this government called into question," Senator Di Natale said from Melbourne.

"Does he care more about himself or the country? That's the question."

- With AAP