Malcolm Turnbull has declared he stands by his blistering criticisms of Barnaby Joyce’s extra-marital affair, despite the furious Nationals leader saying the Prime Minister’s performance was “inept” and had “caused more harm”.

Amid calls for the PM to cancel his trip next week to the US, Mr Turnbull said he understood it was a “very stressful time” for Mr Joyce.

But he did not back away from his comments on Thursday evening, when he suggested Mr Joyce had “appalled all of us”, instead saying twice that he stood by those criticisms.

Only an hour after the Nationals leader publicly blasted him at a snap press conference, Mr Turnbull also stressed he was not seeking to influence the junior Coalition partner to depose their leader.

Mr Turnbull was bombarded with questions about the deepening feud with Mr Joyce, which he declined to answer while standing alongside Tasmanian premier Will Hodgman at a local media event in Launceston.

He did say he had not spoken to his deputy since the extraordinary press conference on Friday morning.

“I have not sought in any way to influence the deliberations of the National Party,” Mr Turnbull said.

“Neither I nor my colleagues have made any criticism of the National Party by expressing views of disapproval or criticism of Barnaby’s own conduct.”

Opposition Leader Bill Shorten labelled the development a “full blown political crisis”, saying Mr Turnbull and Mr Joyce were “at war”.

Mr Shorten said Mr Turnbull’s move to ban sex between ministers and their staff was a “complete smokescreen”, though he said Labor would look at the details.

“What has to happen for the Australian people is the Prime Minister needs to sack his Deputy Prime Minister,” he said.

“Mr Turnbull keeps saying he is in coalition, there is nothing he can do about Barnaby Joyce. He appoints the members of his cabinet. He should get in the car, drive down to see the Governor-General and say Barnaby Joyce is sacked.”

In rare scenes, Mr Joyce escalated the government’s internal turmoil on Friday morning at an impromptu press conference at Parliament House.

Mr Turnbull, who was holding an earlier doorstop interview in Hobart at the time, was unable to tell journalists why Mr Joyce had called the press conference.

The extraordinary tit-for-tat led Liberal MP Kevin Andrews to call on Mr Turnbull to abandon a trip to the United States next week in order to patch things up with Mr Joyce.

“Please gentlemen, sit down together and sort this out,” he told Sky News.

“Mr Turnbull should not be going to America until this has been sorted out. And Mr Joyce should be where he’s needed to be to sit down and have that conversation with Mr Turnbull.

“Otherwise, this circus is just going to continue.”

Treasurer Scott Morrison strongly backed Mr Turnbull’s comments from Thursday.

Asked if Mr Joyce should quit, Treasurer Scott Morrison told 3AW Radio: “That’s for Barnaby to decide.”

Nationals MP Darren Chester, who was demoted to the backbench by Mr Joyce on Friday, fronted media in Canberra to discuss road safety, but was bombarded with questions on the feud.

He would not comment on the spat, saying the government needed to “settle down” and “focus on the job”.