The Turnbull government wants four MPs to resign on Wednesday after the High Court disqualified Labor senator Katy Gallagher over her dual citizenship.
Attorney-General Christian Porter says it's time for Labor MPs Susan Lamb, Justine Keay and Josh Wilson, as well as independent Rebekha Sharkie to stand down, given their British ancestry.
Federal Labor leader Bill Shorten earlier on Wednesday refused to say what his party would do if the ruling went against Senator Gallagher.
"If the High Court sets a new precedent, the Labor Party will deal with it," Mr Shorten told ABC TV.
When pressed on the issue, he said, "If the interpretation of the current law changes, we'll consider what we've got to do."
Cabinet minister Christopher Pyne called on Mr Shorten to ensure his MPs stand down ahead of by-elections.
"There's no need to refer these members to the High Court," he insisted.
"That would be more waste of taxpayers' money. It would be more delay and take more time when there is an unambiguous decision at the High Court today."
Senator Gallagher, who represents the ACT, argued she took every possible step to renounce her British ties to ensure her eligibility to run for parliament at the 2016 election.
She could re-enter parliament through a newly-created lower seat in the territory, and is expected to be replaced in the Senate by fellow Labor candidate David Smith.
Ms Sharkie, of the Centre Alliance, is taking urgent legal advice, but believes her circumstances are materially different to Senator Gallagher's case.
Mr Porter said she was in exactly the same boat as the Labor MPs.
A government spokesman told AAP there were no doubts over coalition MPs Julia Banks, Jason Falinski, Alex Hawke and Nola Marino, who Labor sought to refer to the High Court last year.
The spokesman said they had all been cleared of dual citizenship before nominations closed.
Former Tasmanian senator Jacqui Lambie ruled herself out of running as a candidate in a possible Braddon by-election to replace Ms Keay, as she intends to recontest the Senate.
Crossbench senator Derryn Hinch said "of course" all MPs in similar circumstances to Senator Gallagher should resign if the High Court found against her.
Greens senator Peter Whish-Wilson said Australians were already cynical about federal politics and Labor needed to do the right thing.
"Get this situation cleared up, don't let it drag on," he told reporters in Canberra.
"We don't want to see more High Court cases, we don't want to see more confusion and more uncertainty."