Former prime minister Tony Abbott has demanded Labor leader Bill Shorten prove that he renounced his British citizenship, saying, "show it or shut up".

Key points: Former PM produces letter from the British Government from 1993

Former PM produces letter from the British Government from 1993 Pauline Hanson joins call for Labor figures to produce paperwork

Pauline Hanson joins call for Labor figures to produce paperwork Other Labor parliamentarians under the spotlight include Penny Wong and Sam Dastyari

Mr Shorten' s father was born in England but the Labor leader argues he is eligible to sit in Parliament because he gave up dual citizenship.

Mr Abbott said Mr Shorten should show his letter of renunciation "or shut up".

"His father was born overseas. He says he has renounced his British citizenship. Well, show it or shut up," Mr Abbott said.

Mr Abbott, who was also born in England, produced a letter from the UK Government showing he renounced his own British citizenship in 1993.

Labor MPs have repeatedly refused to produce documents backing up their claims about citizenship, saying no-one has produced evidence that anyone is in breach of the rules.

Labor's National Secretary Noah Carroll insisted that every member of the Labor caucus has been properly elected because the Labor Party has an extensive and exhaustive process for ensuring constitutional requirements are met.

Mr Carroll said it is a critical part of the nomination process and candidates are not nominated by the ALP without being cleared.

One Nation leader Pauline Hanson also called on Labor figures including Mr Shorten, Penny Wong and Sam Dastyari to produce the paperwork to prove they were eligible to be in Parliament.

"You have got quite a few on the Labor side, put it to bed," she said urging them to produce documentation.

Senator Wong has said she was well aware when she stood for Parliament that she would have to renounce any rights she may have had to Malaysian citizenship, and did so prior to nominating.

Senator Dastyari has said he was born an Iranian citizen but had hired two legal teams to ensure he was eligible to be in Parliament.

More senators referred to High Court

While the arguments rage about eligibility, two more senators have been referred to the High Court to decide on their circumstances.

The High Court sitting as the Court of Disputed Returns will consider if NXT party leader Nick Xenophon and Nationals senator Fiona Nash are eligible.

Senator Xenophon's father is from Cyprus, which was a British colony until 1960. It meant he retained a form of British citizenship — and passed it onto his son.

Attorney-General George Brandis said Senator Xenophon had done the right thing but argued he believed the High Court would find Senator Xenophon had been validly elected.

"If Nick Xenophon is an Englishman then the Pope is a Methodist," Senator Brandis said, citing the Prime Minister's recent comments.

Senator Nash potentially has dual citizenship because her father was born in Scotland.

Labor argued she should stand aside from her ministerial duties until the court decides, in the same way that her Nationals colleague Matt Canavan did.

Greens leader Richard Di Natale told the Senate that Senator Nash should have gone further than that and resigned from the Parliament in the same way Scott Ludlam and Larissa Waters did when they discovered their dual citizenship.

Senator Di Natale criticised Senator Nash for only revealing her potential dual citizenship minutes before the Upper House rose for a fortnight.

He described it as "tawdry", while Justice Party Senator Derryn Hinch called it a "dump and run number at five minutes to midnight".

Senator Brandis strongly defended the timing of Senator Nash revealing to the Parliament that she likely had dual citizenship.

He said she spoke in the Senate less than an hour after he and the Prime Minister had seen the Solicitor-General's advice about Senator Nash.

ACT Labor senator Katy Gallagher has told the Senate this morning that she has legal advice that she is not an Ecuadorian citizen.

Senator Gallagher's mother was born in Ecuador in 1943, but she said legal advice showed that does not give her any rights to citizenship of Ecuador.

Other parliamentarians including Deputy Prime Minister Barnaby Joyce have already been referred to the High Court to decide if they were ineligible because of dual citizenship.

Labor argued Mr Joyce should stand aside until that decision was made.

But he again rejected that and said the public was getting angry with the way the ALP was handling the issue.

"This is not helping Labor," Mr Joyce said.

"People are getting angry with it … [they] think it is a clowns' outfit in the Labor Party.

"You hold office until such time as death or you resign or the High Court finds otherwise … people understand that, that is how the laws work.

"It is before the High Court, let the High court make its judgement."

The Senate has today rejected a motion put by Senator Hanson for a review of all senators to determine if they are eligible to be in Parliament.