Prime Minister Malcolm Turnbull and his deputy Barnaby Joyce have held crisis talks in Sydney after publicly criticising each other in separate press conferences earlier this week.

The pair met for over an hour on Saturday and agreed they needed to work together, the ABC is reporting.

The ABC understands that during their meeting Mr Joyce expressed concerns about the forcefulness of Mr Turnbull’s statements on his private life.

On Thursday, Mr Turnbull offered a scathing assessment of Mr Joyce’s affair with a staffer, describing his actions as a “shocking error of judgment” and causing “a world of woe”.

Mr Joyce returned fire a day later, describing Mr Turnbull’s comments as “inept”, “unnecessary” and “hurtful”.

Earlier on Saturday, former prime minister Tony Abbott waded into the public leadership stoush engulfing the coalition government, taking a veiled swipe at Malcolm Turnbull.

Speaking in Melbourne, Mr Abbott said the prime minister — as leader of the Liberals — should not publicly comment on the leadership of the Nationals under Barnaby Joyce.

“The general rule I always observed was that one party doesn’t give another party public advice,” Mr Abbott told reporters.

“The last thing anyone wants is for politicians to be talking about themselves,” Mr Abbott said.

Barnaby should go to the backbench

Liberal senator Ian Macdonald said Mr Joyce knew his actions were damaging the government, and he should spend time on the backbench.

“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.”

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.”

On Friday, Nationals MP Andrew Broad said that while Barnaby Joyce had made an error of judgment, his leadership of the Nationals remained safe for now.

“But I’m still waiting to see if there’s been an abuse of power. If I see that and it’s clear, then I’ll be one of the people talking about what should be the action as a result of that,” he told the ABC.

-with ABC/AAP