A video of two nurses claiming they would kill Israeli patients shows the need for a "national conversation" on migration and citizenship, Peter Dutton says.
Police are examining whether to lay charges against the NSW nurses, one of whom has been identified as an Afghan refugee who recently acquired Australian citizenship.
The case highlighted the need for debate on the "inadequacies" of Australia's migration system, Mr Dutton said, noting the government was heavily restricted in its ability to strip people of their citizenship.
"When we have somebody like this who gets through the net, obviously has breached his obligation about a loyalty to our country when he became an Australian citizen, and yet he has the ability to stay in our country, it should be of deep concern to every Australian," Mr Dutton told 2GB radio on Thursday.
"(It's) about how we can say to these people, 'if you don't share our values, if you're here and you're enjoying the welfare system and you're enjoying free health and free education, then at the same time you hate our country, well, I don't think you've got a place here'."
Labor cabinet minister Anne Aly accused Mr Dutton of "hijacking" a conversation about anti-Semitic hatred.
"I'm a bit angry that this conversation about anti-Semitism has been conveniently turned into a conversation about immigration. As if somehow, the two are connected," Dr Aly told ABC TV.
"I think that's a very deliberate political ploy by Peter Dutton."
There was a need to look at whether dual citizens should be stripped of their Australian citizenship if they "breached" the nation's trust, Liberal frontbencher Dan Tehan said.
As home affairs minister in the former coalition government, Mr Dutton drafted laws seeking to strip the citizenship of dual nationals suspected of engaging in terror activity overseas.
They were later ruled by the High Court to be unlawful.
His comments come a day after NSW state Liberal MP Kellie Sloane, whose Vaucluse electorate has a large Jewish community, said perpetrators of anti-Semitic crimes should be deported.
She insisted she was not specifically referencing the two nurses, who were later identified as Australian citizens.
