Scott Morrison has been rocked by a cabinet leak revealing his most senior colleagues rejected his plan to introduce legislation for a corruption watchdog, as he scrambled to rustle Coalition support for his signature religious discrimination laws.

The Prime Minister floated the idea on Monday during a cabinet meeting as he sought to grapple with competing demands from a restive and frustrated backbench on religious discrimination and the government's refusal to advance an integrity commission.

The cabinet meeting, first reported in The Australian, has been described to the ABC as a terse exchange over the merits of the PM's proposal. 

One minister said the PM faced some hostility to the idea, given the proximity of the next election.

The Prime Minister told colleagues that pressing ahead with the long-promised integrity commission — by presenting a bill to parliament — might help some win re-election.

Though some ministers, including ally Stuart Robert and Senate Leader Simon Birmingham, support the idea of putting a corruption commission on the legislative agenda, others stridently disagreed with the Prime Minister's judgement.

The PM's view was firmly rejected, with ministers including Communications Minister Paul Fletcher arguing strongly against the plan. 

"The view is that because we are so close to the election, the government would quickly lose control and we would end up with a NSW-style ICAC, or a star chamber, which we are all united in opposing," a different cabinet minister said.

A minister said there was some "overlap" between backbenchers' varying demands on religious discrimination laws and their push for a federal integrity commission.

It is understood Tasmanian Liberal MP Bridget Archer was raised in the cabinet discussion, given she had not only publicly declared support for an integrity commission but was also signalling she would cross the floor to oppose the government's religious discrimination laws.

A cabinet minister said he was dismayed the confidential details of the meeting had been leaked to the media and questioned the leaker's motive.

Mr Morrison is the longest serving prime minister since John Howard and has prided himself on maintaining cabinet solidarity.

Ministers believe the leak is calculated to damage him and wonder what the ultimate objective might be.

Although no-one seriously believes his leadership is under immediate threat, one minister pondered what opportunity there might be next week when the House of Representatives reconvenes and many senators are in Canberra for estimates hearings.

Mr Morrison is at his lowest ebb as PM. His authority has been diminished by his failure to deliver a 2019 election commitment on religious discrimination, aggravated by the rebellion of five Liberal MPs on the floor of parliament.