Candidates in five by-elections will need to publicly reveal their citizenship status when they nominate under new election rules.
Prime Minister Malcolm Turnbull rejected calls for a referendum to change the constitution after the dual citizenship crisis, but he flagged urgent changes before the upcoming by-elections.
He said there would not be enough time between now and a federal election, due by May 2019, for a referendum.
Special Minister of State Mathias Cormann said new rules will be ready before the by-elections in WA, South Australian, Queensland and Tasmania, which do not yet have a date.
Candidates will have to give their citizenship information to the Australian Electoral Commission.
"The information will be available for public scrutiny prior to any relevant election," Senator Cormann said.
However, the AEC won't be given the power to adjudicate the eligibility of candidates.
A cross-party committee of MPs released a report calling for a referendum to change a constitution it believes is stuck in 1901.
But committee chair Linda Reynolds said even though the report called for a referendum the prime minister was correct that the time wasn't right.
"We have noted that the pre-conditions for a successful referendum don't yet exist," Senator Reynolds told AAP.
"It will take some time, maybe many months, if not years."
The committee found more than 50 per cent of Australian voters were likely ineligible to run for parliament, providing a strong reason to change the constitution.