The Greens have called for all federal MPs to be subject to a citizenship audit, with Matt Canavan vowing to fight his ineligibility in court.
The Queensland senator resigned from cabinet on Tuesday after it emerged his mother had signed him up to become an Italian citizen in 2006.
She informed him of his status as an "Italian citizen abroad" on July 18 having seen media reports about the ineligibility of Greens senator Larissa Waters and Scott Ludlam which forced them to quit parliament.
Under Section 44 of the constitution a person is disqualified from being elected if at the time of their election they are a citizen of "a foreign power" or otherwise have an "allegiance, obedience or adherence to a foreign power".
Greens leader Richard Di Natale said on Thursday he had written to the Senate President and House Speaker calling for an audit to immediately establish the eligibility of all members of parliament.
Senator Di Natale said the constitution was clear that people with dual citizenship were ineligible to stand and Senator Canavan should do the "honourable" thing and resign from parliament.
"We can't have one set of rules for ministers within the Turnbull government and another set of rules for everybody else," Senator Di Natale told reporters in Melbourne.
Senator Canavan told reporters in Rockhampton while he felt it appropriate to resign from the ministry, legal advice led him to conclude he was not in breach of the constitution.
"I did consider not continuing on, given the circumstances of other cases, but I base my decision very much on that legal advice that we've been provided which provides grounds that I have not breached section 44," he said.
"I think it's important we let that process run now and let the court make its decision."
Senator Canavan said he was aware his mother had applied to become an Italian citizen but he had no knowledge or suspicion of what had occurred 11 years ago until last week.
"I've never signed a document, given consent or have any knowledge of these matters until last week."
Asked whether he was aware his mother had been receiving Italian election voting papers in his name for the past decade, he said he had never received any correspondence from Italian authorities.
Labor frontbencher Jim Chalmers said the government should reveal whether there were clouds over any other coalition MPs in terms of their dual nationality.
The federal opposition also wants Senator Canavan to reveal his documentation, however he says all relevant material will be provided to the court.