Liberal junior minister Alex Hawke has rejected claims he could be a dual citizen, as both the government and Labor again slammed the Greens idea for an audit to end the crisis dogging parliament.
Mr Hawke, the assistant immigration minister, dismissed a suggestion he is a dual citizen, saying he was born in Wollongong and has never held Greek citizenship through his mother, who moved to Australia in the 1950s.
"I am an Australian citizen only and have never held or acquired or sought Greek or any other citizenship," he told News Corp Australia.
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A person acquires Greek citizenship at birth "if said person is born to a parent of Greek nationality", whether it is activated or not. But Greek citizens need to be registered in the Records of a Municipality of the Hellenic Republic, News Corp reported.
The crisis has so far claimed five senators, including Stephen Perry, the former Senate president, as well as deputy prime minister Barnaby Joyce who is now fighting a by-election in his seat of New England.
Greens Leader Richard Di Natale said these extraordinary circumstances must be resolved to allow the parliament to "put this mess behind us".
His idea of an audit of all members and senators would be conducted through a cross-party select committee, which would co-opt lawyers with immigration expertise and individuals who have question marks hanging over them would be referred to the High Court.
"We have to start to restore some integrity in the nation's parliament," he told ABC television.
Senior Labor frontbencher Doug Cameron said the Greens had no credibility on the issue having lost two senators and deputy leaders.
He said Prime Minister Malcolm Turnbull must show some "backbone and leadership" and Opposition Leader Bill Shorten had offered to work with the government towards something that satisfied the parliament.
Finance Minister Mathias Cormann said it was "crazy" to suggest that an audit was an appropriate way forward.
"We don't want to get ourselves into a situation where we have got this witch hunt type, lynch mob type justice," he told Sky News.
"We are not going to make a blanket assumption that everybody is in breach and that everybody has to prove their innocence."
Government frontbencher Kelly O'Dwyer accused Mr Shorten of politically smearing everybody.
"The Australian people are actually really sick of this," she told ABC television.
The Senate next sits on November 13. The House does not sit again until November 27.
