Prime Minister Malcolm Turnbull has praised Liberal MP John Alexander for doing the "honourable thing" and resigning following doubts over his dual citizenship status.

The member for Bennelong has confirmed there is a high likelihood he holds British citizenship and resigned on Saturday, a day after notifying Mr Turnbull of his decision.

"John's done the right thing, the honourable thing," Mr Turnbull told reporters in Da Nang, Vietnam, where he is attending the APEC summit.

"He told me that he was no longer sufficiently satisfied ... that he was not a UK citizen."

PM insists no need to cut short Asia summit tour to return home and deal with JA’s resignation creating minority govt @SBSNews #auspol pic.twitter.com/HZRHwytfKG — Daniela Ritorto (@danielaritorto) November 11, 2017

Earlier this week Mr Alexander sought advice on whether his English-born father Gilbert Alexander had conferred UK citizenship, despite arriving in Australia in 1911.

Mr Alexander said he hadn't received official confirmation of his dual citizenship, but said the "balance, the probability of evidence is that I most likely am".

"The obligation that I have is that once I do not hold the view that I'm solely Australian I must resign. Having determined that late yesterday, to my satisfaction, just my choice, I felt I had to resign," he told reporters in Sydney.

Now he will contest his seat and stand again for parliament in an upcoming by-election, he said.

It follows Barnaby Joyce's decision to recontest his seat of New England in a by-election after he was forced to step down over his New Zealand citizenship.

Mr Turnbull has urged Labor MPs with any doubts over their citizenship status to consider doing the same thing and take their case to the High Court.

"The High Court determines who is eligible to sit in the House of Representatives, not the Labor Party," he said on Saturday.

It is the latest in an ongoing saga which may see politicians in half a dozen federal seats sen back to the polls.

PM: John Alexander has done the right thing. He's no longer satisfied that he is not a UK citizen — Rashida Yosufzai (@Rashidajourno) November 11, 2017

Another Turnbull government MP, Nola Marino, may be ineligible for parliament after questions she may hold Italian citizenship through marriage.

Ms Marino married her husband Carmelo 'Charlie' Marino in Western Australia in 1972.

He is an Italian citizen by birth, but if he naturalised as an Australian before 1972, he would have lost his Italian citizenship and not have automatically passed it onto his wife.

Fairfax reported on Saturday that Mr Turnbull's plan for a new disclosure regime to end the citizenship uncertainty may have a gap, with dual citizenship through marriage not under consideration.

On Friday Mr Turnbull received Greens support to refer all MPs with "legitimate question marks" over their citizenship to the High Court.

But the Greens will still push ahead with a motion in the Senate on Monday to set up an independent audit of all 226 MPs to end the citizenship crisis and restore stability.

The prime minister has proposed that all MPs lodge details, on a public register, of their family history and renunciation of foreign citizenship by December 7.