EXCLUSIVE

Foreign Affairs Minister Julie Bishop has sought to downplay an extraordinary cabinet leak showing deep divisions in Tony Abbott's government over national security.

Labor says the leak is "groundbreaking" in its scope and detail, and highlights the prime minister's erratic leadership and dysfunctional frontbench.

Fairfax Media on Saturday published a blow-by-blow account of a cabinet split over a controversial proposal to strip Australians of their citizenship.

The government is pursuing new laws that would give it the power to strip dual nationals of their citizenship if they engage in terrorism, but the leak shows Prime Minister Tony Abbott and Immigration Minister Peter Dutton wanted to go further.

Their proposal would allow the minister to revoke someone's Australian citizenship even if it's the only one they have, as long as there are grounds to believe that person is able to become a national of another country.

Ms Bishop was among at least half a dozen ministers who strongly objected to the proposal at the Monday meeting. Malcolm Turnbull, Barnaby Joyce, George Brandis, Christopher Pyne and Kevin Andrews are also believed to have spoken against it.

It was also revealed that the matter was not listed on the cabinet agenda and there was no written proposal given to ministers. But the idea is contained in a citizenship discussion paper that has now been made public.

Ms Bishop is due to attend a meeting on Tuesday in Paris of senior officials from 22 countries about the conflicts in Syria and Iraq.

On Saturday, Ms Bishop said the discussion paper was the right way to test the proposal, calling for a national conversation. But she conspicuously refused to outline her personal view, calling it a "complex issue that we need to discuss".

She denied she was the leaker and sought to downplay the significance of the breach.

"I don't think it's the first occasion in the history of Australian politics that there's been an apparent leak from a cabinet meeting," she told reporters.

Nor was it surprising that there was a "robust debate" around the table, she said.

She denied there had been a breakdown in trust between her and the prime minister.

"Absolutely not," she insisted. "The prime minister and I have worked exceedingly closely together on all matters to do with counter-terrorism."

But Labor frontbencher Tony Burke seized on the leak, which he said contained more details than most official cabinet minutes.

"To see something of this order is quite groundbreaking," he told reporters in Sydney.

The leak gives lie to Mr Abbott's pledge to run a collegial and consultative cabinet, he said.

"This is an erratic prime minister leading a dysfunctional and divided cabinet. And on national security issues we do need better than that."

While the proposal was unpopular in cabinet it has not been completely abandoned, and coalition backbenchers are urging Mr Abbott to stick with it.

Thirty-seven MPs have co-signed a letter to the prime minister in which they call on him to stand by his tougher plan, which is modelled on UK laws.

"We write to bring to your attention our views regarding the government's proposal to introduce legislation on the revocation of citizenship," the letter reads.

"We ask that you ensure the legislation to be presented to Parliament includes provisions to cover not only dual nationals but those eligible for the citizenship of another country."

One of the organisers of the backbench campaign, Victorian MP Dan Tehan, says the government must look "incredibly seriously" at the issue.

He says such laws would be used very rarely and there would be judicial safeguards in place.

"But we do need to be able to act when people are committing treason against our nation," he said.