Federal Treasurer Josh Frydenberg will not face a by-election in his Melbourne seat of Kooyong after a legal challenge questioning his eligibility to sit in Parliament was struck down.

Key points: Mr Frydenberg's lawyers were not able to provide documents showing his mother's family had given up their Hungarian citizenship, but the Federal Court justices found that the family had

Mr Frydenberg's lawyers were not able to provide documents showing his mother's family had given up their Hungarian citizenship, but the Federal Court justices found that the family had They found Mr Frydenberg's mother would have been "stateless" when she left Hungary in 1949

They found Mr Frydenberg's mother would have been "stateless" when she left Hungary in 1949 Michael Staindl, a voter in Mr Frydenberg's electorate who brought the challenge to court, said he was disappointed in the outcome but respected the ruling

On Tuesday the Federal Court sitting as the Court of Disputed Returns ruled on a Section 44 challenge brought by Michael Staindl, a voter in Mr Frydenberg's electorate in Melbourne's eastern suburbs.

Mr Staindl's lawyers had argued the Australian-born Treasurer was not eligible to sit in the Parliament because he was also entitled to Hungarian citizenship through his mother, Erica Strausz.

Ms Strausz was born in Budapest in 1943 but left the country with her family in 1949.

Lawyers for Mr Staindl had argued the family had not renounced its claim to Hungarian citizenship when Mr Frydenberg was born in 1971.

Section 44 of the constitution does not allow dual citizens to sit in Parliament.

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Family fled Hungary amid 'catastrophe and anti-Jewish violence'

During the case, the court heard from several experts in Hungarian law and history.

At the time that Ms Strausz's family fled Hungary it was under communist rule, imposed after the Second World War.

In dispute was whether the Strausz family members had given up their citizenships.

"It is against this background of catastrophe and anti-Jewish violence and terror that the proof and assessment of law and legal status of Jewish Hungarians, such as the Strausz family, wishing to leave Hungary for a new life somewhere, must be undertaken," the ruling says.

While Mr Frydenberg's lawyers had not been able to provide documentation that his mother's family had given up Hungarian citizenship, the justices found the family had.

Ms Strausz became a naturalised Australian in 1957.

"We accept that the reality in Hungarian law in 1949 ... was that by leaving Hungary the Strausz family brought an end to their Hungarian citizenship," the ruling states.

"The evidence is sufficient to conclude that upon leaving Hungary in 1949 the Strausz family lost or renounced any citizenship of Hungary and were stateless."

Mr Staindl had also tried to argue that when the communist regime fell in Hungary in 1989 at the end of the Cold War, the family's rights to citizenship were revived.

"There is no evidence whatsoever that somehow the political changes nearly two generations later, in 1989, had any effect upon that legal reality as it existed in and after 1949," the justices wrote.

'Section 44 is a hash'

Mr Staindl, a climate activist, said he was disappointed in the outcome but that he respected the ruling.

But he said questions remained.

Michael Staindl challenged the eligibility of Mr Frydenberg to sit in Parliament. ( ABC News: Karen Percy )

"By Mr Frydenberg's own evidence he twice enquired of the Hungarian embassy what he needed to do to clarify this, in 2017 and 2019," Mr Staindl said.

"He was sent information, very simple information, the required documents that he need to complete and in both cases he refused to do that."

Mr Staindl said he had endured abuse for taking on the case - including being accused of being anti-Semitic - but he said MPs needed to obey the law.

"Section 44 is a hash - it absolutely needs to change," he said.

"This dual citizenship rule needs to be looked at in a much more enlightened and intelligent way.

"But we also need our leading legislators to follow the law as much if not more than anyone else."

Mr Frydenberg has been the member in the safe Liberal seat since 2010.