Government MPs are divided over whether to pursue new rules to deport members of terrorist organisations if they hold dual citizenship.
Tasmanian Liberal Michael Ferguson told the coalition partyroom on Tuesday that those found guilty of terrorism were un-Australian and should be deported if they held dual nationality.
Victorian MP Petro Georgiou and Queensland senator George Brandis reportedly rejected the call during the meeting, but NSW Liberal backbencher Bronwyn Bishop, who missed the partyroom discussion, on Wednesday said it was an issue worthy of examination.
"I think the question of citizenship and the sort of terrorist acts that we are now dealing with is one we're going to have to grapple with," Ms Bishop told reporters.
"At the moment, it's not being discussed, but I think it's one that has to be discussed.
"I think I want to hear the discussion about it - I think it's an important question that we have to examine."
West Australian Liberal Wilson Tuckey also said he was open to the idea.
"I'm open-minded on it until I have proper advice as to what the effects might be," Mr Tuckey said.
"I think the Australian community, or segments thereof, are a bit concerned at the moment as to the speed with which people can achieve citizenship and the benefits that flow, if they then take up illegal activities."
But fellow West Australian Liberal Dennis Jensen, who was born in South Africa, said he was not in favour of the suggestion.
"What you end up with is two levels of citizenship - one of native-born Australians and (the other) of people that are born overseas," Dr Jensen said.
"I certainly have an issue, however, with people that swear oaths or make affirmations ... in their application for citizenship that are false.
"Now I think that there's potential there if there've been false statements made to support citizenship.
Asked if he would support deportation, Dr Jensen said: "Not as a policy, no".
Opposition foreign affairs spokesman Kevin Rudd said he had not considered the proposal.
"Well, a Liberal Party backbencher ventilating in the party room doesn't equal federal government policy," he said.
"I haven't considered any such proposal."