Malcolm Turnbull is concerned six Iranian refugees have been allowed to stay in Australia after holidaying in the country they fled out of fear for their lives.
The Administrative Appeals Tribunal reportedly has overturned Immigration Minister Peter Dutton's decision to cancel their visas and deport them.
The prime minister said Mr Dutton was reviewing the cases and considering his next step.
"But, plainly, people who are claiming that they are subject to persecution in Iran but are travelling back on holidays there, clearly that is not a credible claim," Mr Turnbull told reporters in Adelaide on Tuesday.
"I absolutely understand (people's concerns) and so does the government."
While refusing to comment on this particular instance, Mr Dutton said such cases were "infuriating".
"There are many cases that I look at where, on the facts available to me, you shake your head," he told 3AW's Neil Mitchell.
"People who are being slaughtered in the Middle East now that we would want to give protection to, they're the ones being displaced by people who are seeking a better economic outcome."
Australia, bound by international conventions, can't send people back to a country where they face persecution.
Mr Dutton said Iran, in particular, won't take people back unless they return voluntarily.
"That's the dilemma - and the rub against that, of course, is that we don't have indefinite detention."
The federal government has deported between 500 and 600 people over the past year, including 136 bikies in the last 18 months.
Outlaw motorcycle gang members have been the top targets, with sexual offenders also a priority.
Six people involved in Melbourne's Apex gangs have had their visas cancelled, with seven others under review.
"These are serious offenders - people who have committed rapes, people who have committed armed robberies," Mr Dutton said.
Mr Dutton admitted to being frustrated with the lengthy and costly appeals process, following reports 39 per cent of his decisions or those by delegates have been overturned by the AAT in the past year.
He suggested the independent tribunal, whose members are appointed by the government of the day, is influenced by politics.
The government has not renewed the tenure of some members who were appointed during the Rudd-Gillard years, and made some fresh appointments.
"So the rejection rate will change over time," Mr Dutton said.
