Australia needs to have a conversation about citizenship: Bishop

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

The foreign minister also 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.