Malcolm Turnbull's government has been rocked by the resignation of Senate President Stephen Parry - the first Liberal to be engulfed in the citizenship debacle.
Senator Parry received advice from the Home Office on Wednesday that he held British citizenship through his UK-born father.
It put the Tasmanian Liberal senator in a similar position to that of Fiona Nash, who was found by the High Court last Friday to be disqualified under section 44 of the constitution because of her dual citizenship through her Scottish-born father.
"Now that the High Court's recent ruling has given absolute clarity to the meaning and application of section 44(1) ... I will submit my resignation as both president of the Senate and as a senator for Tasmania to his excellency the Governor-General tomorrow," he wrote in a letter to senators on Wednesday.
Senator Parry is widely expected to be replaced by former minister Richard Colbeck, who has been working as a tourism lobbyist and was given the unwinnable sixth spot on his party's Senate ticket in 2016.
Tasmanian Liberal powerbroker Eric Abetz, who is credited with helping push Mr Colbeck down the ticket last year, said on Wednesday he believed the former tourism minister would "hit the ground running".
Mr Turnbull, who is expected to return from Israel on Thursday, also faces a stoush over who replaces Senator Parry 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.
However, Senator Abetz said the president's position would be filled by a Liberal, in line with convention.
Leader of the government in the Senate George Brandis thanked Senator Parry for his service, saying he brought authority, dignity and fairness to his role as president. Senator Parry's ineligibility will be referred to the High Court as the Court of Dispute Returns.
Senator Brandis doesn't anticipate any delay in making orders for a special count of Tasmanian Senate ballot papers.
Meanwhile, debate is raging over whether a citizenship audit is needed of all MPs to clear the air.
The Greens have the backing of some Labor and coalition backbenchers for an audit, which would involve all MPs providing proof of their Australian-only citizenship to an independent body.
Ms Bishop dismissed the audit idea, saying all MPs had a personal responsibility to ensure they were eligible to stand for parliament.
"We now have a High Court decision which clarifies Section 44 (of the constitution) and every person has responsibility to ensure they're eligible," she said.
Acting Labor leader Tanya Plibersek said the simplest way of addressing this is for every member of parliament and candidate to follow the rules.
"What amazes me is every member hasn't double-checked for themselves and that is the extraordinary thing about the revelation of Stephen Parry," she told reporters.
Greens leader Richard Di Natale said an audit would remove the "huge shadow over parliament" which was destroying people's faith in democracy.
