Bill Shorten has offered an olive branch to the prime minister over citizenship issues relating to Queensland MP Susan Lamb, saying Labor will refer her to the High Court, but only if the government follows suit on its own MPs.
Ms Lamb, the member for Longman, is a British citizen by descent, but the UK Home Office could not process her renunciation before the 2016 election because it could not be satisfied from the documents available that she held the citizenship.
Labor says she took reasonable steps to renounce her status.
Opposition deputy Tanya Plibersek says Labor leader Mr Shorten has again phoned Malcolm Turnbull offering to send Ms Lamb for the court's judgement as long as the government will refer its own MPs who are in similar circumstances.
Mr Shorten later told reporters Mr Turnbull has to compromise.
"Clearly there is doubt over some Coalition MPs. I just believe in one rule for all," he said.
But on Tuesday, government frontbenchers remained adamant that referrals were an issue for the Labor Party alone.
Deputy Prime Minister Barnaby Joyce refused to say at what point the coalition would consider unilaterally referring Labor MPs.
"We're just going to let Mr Shorten find his own juice on this one," he told reporters in Canberra.
Asked whether a bipartisan referral deal was possible, coalition frontbencher Matt Canavan said any offer was just another excuse from Labor to politicise the issue.
"Now the Labor Party are trying to bring in people who have family heritage through the Holocaust," he said, referring to questions surrounding Liberal MP Jason Falinski's citizenship status.
"It's disgraceful behaviour to try and protect their own member."
Attorney-General Christian Porter says the argument for the referral of Ms Lamb has become irresistible and it's likely Mr Shorten will agree to it in the "very near future".
The government is in a position to use its numbers in the lower house to make the referral, after John Alexander retained his seat in the Bennelong by-election.
Speaker Tony Smith has yet to decide on a Batman by-election date after Labor's David Feeney quit over citizenship issues, but it is the government's preference to hold a Longman by-election on the same day.
