There will not be a citizenship audit of federal politicians, with Prime Minister Malcolm Turnbull declaring "we are not going to engage in some kind of national witch hunt".

Key points: Malcolm Turnbull says a citizenship audit would be unworkable

Malcolm Turnbull says a citizenship audit would be unworkable Furious at suggestions Josh Frydenberg is a dual citizen, PM points out Mr Frydenberg's mother was born in a ghetto during WWII

Furious at suggestions Josh Frydenberg is a dual citizen, PM points out Mr Frydenberg's mother was born in a ghetto during WWII Bill Shorten says all politicians should be required to make a declaration to Parliament

The push for an audit further intensified when former Senate president Stephen Parry resigned this week because he has dual citizenship.

Mr Turnbull has rejected the idea, ridiculing it as unworkable.

"Are we saying that we would propose to have somebody interrogate each and every member and senator, examine their genealogy, seek to uncover facts about their parentage that may not even be known to the member or senator?" he asked.

Mr Turnbull said an auditor would then have to establish what complex foreign laws might apply to each person.

He argued the High Court is the only way to determine eligibility.

"The constitution is very clear, every member and every senator has an obligation to comply with it," Mr Turnbull said.

"The High Court has clarified the meaning of Section 44 in respect of dual citizenship and it is up to senators and members to satisfy themselves they are in compliance."

On Friday The Australian newspaper raised questions about whether Energy Minister Josh Frydenberg has Hungarian citizenship inherited from his Jewish mother who left as a small child after World War Two.

"We are not going to have politicians, members and senators tried by innuendo and smear," Mr Turnbull said.

Clearly furious, Mr Turnbull pointed out that Mr Frydenberg's mother was born in a Budapest ghetto in 1943.

"That is where the fascists had pushed all the Jews in together as a prelude to sending them to the gas chamber. She wasn't a Hungarian citizen when she was born, neither were her parents," Mr Turnbull said.

"The Hungarian fascist government, allied with Hitler, stripped Jews of all of their rights, the right to citizenship and the right to life."

Sorry, this video has expired Josh Frydenberg labels Hungarian citizenship possibility as 'absurd'

Turnbull's challenge to MPs

Mr Turnbull argued the burden of proof had to be on the person accusing someone else of having questionable eligibility.

He challenged anyone in federal Parliament who believed another person was ineligible to set out their reasons and convince their colleagues to refer the case to the High Court.

"The Parliament has the power to refer any member or senator to the High Court on this question of eligibility and the High Court alone has the ability to determine it," Mr Turnbull said.

Shortly after Mr Turnbull spelled out his position on the citizenship drama, Opposition Leader Bill Shorten issued a statement saying Labor now supports a process where all politicians make a declaration to Parliament.

But he did not outline how it would work.

He said it had to be robust enough to give people confidence in the process.

"But it must not be allowed to create more legal problems, or in any way undermine the supremacy of the High Court on these matters," Mr Shorten said.