Scott Morrison is standing by his Home Affairs Minister Peter Dutton, despite him escaping a vote of no confidence in parliament by the skin of his teeth.
Australian Greens MP Adam Bandt moved a motion to suspend standing orders on Thursday, in a bid to force a no confidence vote against Mr Dutton.
The chamber narrowly voted down the motion 68-67.
Labor says Mr Dutton must be sacked, for misleading parliament when he originally said he did not know the people an au pair was going to work for before he intervened in her visa process.
It was only later revealed she was planning to work for an old Queensland Police colleague he says he hadn't spoken to for 20 years.
But the prime minister says Mr Dutton is "doing a fantastic job".
"When it comes to border protection, the Labor Party are more interested in protecting Australia from au pairs than they are protecting Australians from violent criminals," Mr Morrison told parliament.
Greens Leader Richard Di Natale believes the Wentworth by-election in October might deliver the final vote needed for a motion against Mr Dutton to succeed.
"The Wentworth by-election will be very important, because it only went down by a vote, so we'll see what happens there," he told Sky News on Thursday.
Australian Associated Press
