Malcolm Turnbull says it's up to federal politicians to dob themselves in if they're worried their citizenship status rules them ineligible to sit it parliament.
The prime minister on Wednesday rejected calls for an audit of all MPs and senators, following the resignation of Senate President Stephen Parry.
Senator Parry received advice from the Home Office that he held British citizenship through his UK-born father.
He is the first Liberal to be enmeshed in the citizenship saga, and follows the disqualification of cabinet ministers Barnaby Joyce and Fiona Nash.
"I'm disappointed Senator Parry didn't make public this issue some time ago, quite some time ago," he told reporters in Jerusalem.
"He chose to delay his reporting of it, he should've reported it much earlier and it could've been referred to the High Court together with the other matters that were dealt with."
The Greens and some Labor and coalition backbenchers are now calling for an audit of all members' citizenships to clear the air.
But Mr Turnbull dismissed the idea.
"What is an audit? Does that mean somebody is going to undertake extensive genealogical research on every member of parliament and senator? Undertake extensive research into foreign laws?" he said.
"I expect every member and senator to take their obligation very seriously. If they feel they're not in compliance with the constitution to say so."
Senator Parry is widely expected to be replaced by former minister Richard Colbeck.
But Mr Turnbull may need to play umpire over who replaces him as president.
Nationals MPs have been lobbying hard for NSW senator John "Wacka" Williams to fill the role, partly in retribution for Mr Turnbull putting Julie Bishop in the acting prime minister role rather than the Nationals parliamentary party leader Nigel Scullion.
It seems unlikely, though, with the prime minister saying the role was typically filled by a Liberal.
"The Liberal party, as the larger party in the coalition, has always chosen from its senators the president when in government."
Mr Turnbull will arrive in Perth on Thursday evening ahead of a regional trade conference and meeting with German President Frank-Walter Steinmeier.
Meanwhile, the High Court is due to instruct the Australian Electoral Commission on the replacement process for Ms Nash, Scott Ludlam, Larissa Waters and Malcolm Roberts.
It is expected the replacements will be known before the Senate resumes on November 13.
The South Australian parliament will determine who replaces retired senator Nick Xenophon on November 14.