A meeting between the Prime Minister and Opposition leader Bill Shorten on Wednesday failed to find a solution to the problem, with both parties stressing the need to prevent the issue spilling into the new year.
"[Shorten] wants to exploit this issue, he wants to prolong that, he does not want to resolve it," Malcolm Turnbull told Seven Sunrise on Thursday morning.
"He had no changes to propose, no wording. We spoke for two hours and he could not clarify or articulate the changes that he wanted."
Prime Minister Turnbull reiterated his call for full citizenship status disclosure of politicians, requiring days - not weeks - for those disclosures to be considered.
He was concerned a full independent audit of parliament would take too long.
"I am committed to ensuring that for Christmas we have full disclosure," Mr Turnbull said.
Opposition leader Bill Shorten has said Australia cannot continue into the new year without resolving the dual-citizenship crisis afflicting parliament.
"I have told Malcolm that this crisis has been going on for months so I don't know why he needs more and more days to resolve it," Mr Shorten told Seven's Sunrise on Thursday morning.
"We have demanded a solution and we made constructive progress."
Labor disagrees with the government over how strong a dual-citizenship test for politicians should be.
"There is no point in us coming up with a solution in parliament which then doesn't pass in the courts. That is causing chaos," Mr Shorten told The Today Show on Thursday morning.
"All we are asking for is if your parents or grandparents are born overseas that the parliamentarian takes reasonable steps to investigate and renounce any potential foreign citizenship."
Mr Turnbull and Mr Shorten have agreed that the process needs to be completed by the end of the year, to give all Australians greater certainty about their parliamentary representatives.
Labor is arguing for more details to be publicly disclosed and a December 1 deadline.
But Mr Turnbull says that won't give MPs enough time to do their research and for the parliament to properly scrutinise the information to consider who, if any, to refer to the court.
