The under-siege Deputy Prime Minister, who is about to begin a week of personal leave, blamed a hectic travel schedule that has seen him spend as little as 22 nights at home in a year for being the "substantial cause" of the breakdown of his marriage to wife Natalie.

And Mr Joyce has also hosed down questions about a January 2017 trip by Vikki Campion - his former staffer, turned pregnant partner - who travelled to the Sunshine Coast for one night to help him prepare for an appearance on the ABC's 7.30 program and other media engagements while he was on holidays with his family.

Mr Joyce spoke exclusively to Fairfax Media on Sunday after Prime Minister Malcolm Turnbull sought to quell the civil war inside the Coalition, sparked by the extramarital affair that was revealed nearly two weeks ago.

Mr Turnbull pointedly refused to apologise for his scathing criticism of the Nationals leader but said face-to-face talks on Saturday with Mr Joyce were "frank and warm, friendly, good, constructive".

"There are no issues between the Liberal and National parties at all. None at all," Mr Turnbull said, despite evidence to the contrary such as Nationals MPs publicly criticising the Prime Minister.

"It's always very important to meet, to work through the various challenges and issues that we face but the important thing is Barnaby and I are working closely together as we always have."

The future of the Coalition agreement between the Liberal and National parties has been put at risk by Mr Turnbull's public attack on Mr Joyce's "shocking error of judgment" and Mr Joyce's blistering counter-attack in which he called the Prime Minister "inept" and accused him of causing more harm.

Mr Joyce told Fairfax Media on Sunday that he believed the pair could still work together and that "Malcolm and I are strong personalities" who had both expressed their views in their meeting.

"Like most people in a strong business relationship, there are times you need to discuss your views because that's how you resolve things," he said.

"I don’t believe either of us are the sort of people who whisper behind closed doors - if you have an issue, you confront it head on and that's what we did."

Asked whether he was bracing for more questions from the media about the possible misuse of his entitlements - Mr Joyce has faced questions over an unusually high claim of 50 nights travel allowance in Canberra outside parliamentary sittings, as well as over rent free accommodation from businessman friend Greg Maguire and a function held by his department in Mr Maguire's Armidale function centre - the Deputy Prime Minister was defiant.

“I am and continue to be confident that there has been no misuse of travel or entitlements, nor that any has been or will be found. I base that confidence on the fact that hundreds of inquiries have been made and nothing has been found," he said.

Mr Joyce said that Ms Campion was "most certainly not" his partner when she had travelled to the Sunshine Coast on a commercial flight in January 2017 to help him prepare for media interviews about an outbreak of white spot disease affecting prawns, that she had seen his family while on the trip and had that she had flown back from Brisbane the next day.

“It’s unsurprising that a media adviser would come to help you with media on 730 on a major bio-security outbreak such as white spot," he said.

“There seems be an attitude from certain sections of the media now that any story is a fact, rather than making the facts stack up as a story. No, get your facts straight before you publish.

"When Labor came up with allegations about me being responsible for Greg Maguire's payment [for the use of his function centre in Armidale], I wasn’t, it was my Department."

Senior Liberals want Mr Joyce to stand down over the affair, after nearly two weeks of damaging headlines that have halted the government's momentum and plunged the Coalition into a full-blown political crisis.

Nationals MPs are now openly canvassing a leadership change - which would install a new deputy prime minister - but it remains unclear whether the party room will take the rare step of removing Mr Joyce.

Mr Turnbull insists he can still work closely with Mr Joyce, despite their extraordinary public war of words.

Opposition Leader Bill Shorten repeatedly used the word "inept" and said "the deputy prime minister and the prime minister care more about themselves than they do about the needs of Australians".

Despite the embarrassment the affair has caused the government as a whole, Treasurer Scott Morrison said any change was a matter for the Nationals.

"I think one of the outcomes of yesterday was an understanding that the Prime Minister and the Liberal Party are not in any way intervening in the affairs of the National Party," Mr Morrison told the ABC.

"We're a professional government."

Mr Turnbull made the comments about Mr Joyce's private life as he announced changes to the ministerial code of conduct banning sex between ministers and their staff.

Mr Joyce's affair with Ms Campion started when she was a media adviser in his office and continued when she was shifted to other National party offices.

Nationals MP and Veterans Affairs Minister Michael McCormack - considered the most likely to replace Mr Joyce - did not rule out a leadership challenge on Saturday but said he didn't want to get "too far ahead of myself".

If a change was to occur it would most likely happen at a party room meeting when Parliament returns next Monday.