There needs to be a national conversation about citizenship and changes to laws to keep Australians safe from the growing threat of home-grown terrorism, Julie Bishop says.

The foreign minister also on Saturday denied there had been a breakdown in trust between her and Prime Minister Tony Abbott, following reports cabinet was ambushed by a proposal to strip Australians suspected of terror offences of their sole citizenship.

"We expect there to be a national conversation about the rights and responsibilities of citizenship and about a proposal to strip those who undertake terrorist activities and do harm to Australians of their citizenship," she said.

Ms Bishop denied there had been a breakdown of trust between her and Mr Abbott, after Fairfax reported five cabinet ministers disagreed with a proposal to give Immigration Minister Peter Dutton the power to strip Australian terror suspects of their sole citizenship.

The article quoted ministers raising concerns about the plan, and Ms Bishop as saying she had not seen a discussion paper raised in the meeting.

"The prime minister and I have worked exceedingly closely together on all matters to do with counter-terrorism, foreign terrorist fighters," she said.

"I'm a member of the national security committee, we work extremely closely on these issues."

The government had released a draft discussion paper on the proposal to the public, she said.

"Obviously there are a significant number of legal consequences. It is a complex issue, citizenship is a very serious right and very serious responsibility comes with it," she said.

"It is a discussion we should have in Australia, it's a discussion that's being undertaken in other countries.

"It comes down to a contest of ideas. We want the best public policy we can (have)."