02/11/2017 12:13 AM AEDT | Updated 02/11/2017 7:23 AM AEDT

Stephen Parry Should've Come Clean Sooner: Malcolm Turnbull

Turnbull only found out about Parry's dual citizenship the day the news broke.

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Malcolm Turnbull admits he's disappointed Stephen Parry didn't disclose his dual citizenship and potential ineligibility to sit in parliament sooner.

But the prime minister brushed off the idea of auditing all federal politicians, insisting it was up to MPs and senators themselves to ensure they are eligible for election.

Mr Turnbull delayed his trip to Israel to sort out the mess left by the High Court's decision to disqualify Nationals leaders Barnaby Joyce and Fiona Nash, only to have another fire to put out while overseas.

He only found out on Tuesday - the day the news broke - that Senator Parry was going to resign after receiving advice from the Home Office that he held British citizenship through his UK-born father.

The Senate President is the first Liberal to be enmeshed in the citizenship saga.

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Tasmanian Liberal Senator Stephen Parry was elected President of the Senate on July 7, 2014.

"I'm disappointed Senator Parry didn't make public this issue quite some time ago. I learnt about it the same time as you did, on Tuesday," he told reporters in Jerusalem on Wednesday.

"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 other citizenship-by-descent cases."

He said the matter will have to be referred to the High Court - for a likely very short hearing - when parliament returns on November 27.

Asked whether there should be an audit to ensure there are no more dual citizens in parliament in breach of the constitution, Mr Turnbull wasn't sure how that could work.

"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.

"It's the responsibility of each member and senator to examine their own affairs, form a view and if they feel they are not in compliance with the constitution they should say so."

Nationals MPs have been pushing for NSW senator John "Wacka" Williams to fill the role of Senate President, but Mr Turnbull said that's traditionally be held by a Liberal.

"The Liberal party, as the larger party in the coalition, has always chosen from its senators the president when in government."