Matt Canavan discussed taking out Italian citizenship with his family in 2005 but says he never signed any documents or forms and believed the matter never progressed.
Deputy Prime Minister Barnaby Joyce on Wednesday defended the former resources minister as an "exemplary person" and said Senator Canavan's mother was "at her wit's end" that her son's promising political career had stalled.
Senator Canavan resigned from the Turnbull government ministry on Tuesday night after publicly declaring his mother signed him up for Italian citizenship without his knowledge.
Asked how that could happen given the rigorous application progress required to obtain Italian citizenship, Mr Joyce said: "Well, Senator Canavan has stated to me that he did not complete any forms, so it was a discussion the family had and he thought that's where it's rested. I think they've found the forms and they're unsigned."
When pressed for more details about the family discussions, Mr Joyce said that would be "a question that would be deliberated by the High Court" and would not elaborate further.
"I think it was back in 2005 and any person with memories of things in 2005 has to be given some latitude."
Senator Canavan is a close ally of Mr Joyce and is seen as a rising star within the Nationals.
He will remain in Parliament while the government makes an urgent application to the High Court to determine the matter. The government argues that because Senator Canavan's registration as a citizen was obtained without his consent, his Italian citizenship is invalid and he is not in breach of section 44 of the constitution, which prevents dual nationals from serving as federal MPs.
Mr Joyce said he first became aware of the issue "around about the 18th" of July but "we never believed that this would be the chain of events".
"You can use the hypothetical that if Libya decided they were going to sign me up as a Libyan without my knowledge, that I would be Libyan. It's an absurdity," he said.
No connection to father: Joyce
The Deputy Prime Minister denied Senator Canavan's mother applied for Italian citizenship on his behalf at the same time as his father was sentenced to seven years' jail for fraud.
Bryan Michael Canavan was sentenced to more than seven years' jail in 2007 for embezzling almost $1.6 million from food giant Nestle Australia.
Canavan and other man, Phillip Michael Gardiner, pleaded guilty to two counts of fraud which took place between January 2001 and May 2004.
"I don't particularly want to go into the details of that," Mr Joyce said. "What that can show you is the incredible character of a person such as Matthew Canavan, that he is, you know, in tougher times he has come through as an exemplary character and exemplary person."
The government has no plans to change section 44 of the constitution, which has now claimed three political scalps this month - Senator Canavan and former Greens' senators Larissa Waters and Scott Ludlam.
At the time of the Greens' resignations, Prime Minister Malcolm Turnbull said the failure to clarify their citizenship status before standing for election showed "incredible sloppiness".
Call for Canavan to resign from Parliament
Greens leader Richard Di Natale on Wednesday called on Senator Canavan to resign.
"The advice we received is that ignorance is so excuse," Senator Di Natale said.
"If he is a dual national he is ineligible to stand. I have sympathy for Senator Canavan but our job is to uphold the law. If we don't, what example are we setting for the community?"
Labor leader Bill Shorten said he felt sympathy for Senator Canavan, but called for the Italian consulate in Australia, or Senator Canavan himself, to publicly release all documents relating to his citizenship.
Mr Shorten did not agree there should be a cross-Parliament audit of the status of all MPs, as suggested by One Nation senator Malcolm Roberts.
Senator Roberts has signed a statutory declaration claiming he is not a dual citizenship but will only release his renunciation documents to a parliamentary inquiry.
'No need for an inquiry'
Mr Joyce also ruled out an inquiry to examine the citizenship status of all MPs, saying it was the responsibility of political parties to vet candidates.
Mr Joyce will take over Senator Canavan's ministerial responsibilities for resources and northern Australia. He will be sworn in by Governor-General Sir Peter Cosgrove on Thursday.
The government will move to refer the matter for determination by the High Court when the Senate convenes the week after next on August 8.
