Malcolm Turnbull won't say whether Scott Ludlam will be asked to pay back nine years of salaries and allowances after ruling himself ineligible for office.
The Greens senator on Friday resigned from federal parliament after discovering he still holds New Zealand citizenship.
Under the constitution, a dual national cannot stand for election.
The matter will be referred to the High Court, which is likely to formally disqualify him and order a recount of ballot papers from the 2016 election.
The prime minister hoped it will be dealt with as quickly as possible.
"It's obviously Senator Ludlam's oversight," told reporters on the Gold Coast on Saturday.
"It's a pretty remarkable one when you think about it, that he's been in the Senate for so long."
The former deputy Greens leader was first elected in 2007 and retained his West Australian seat at the 2013 and 2016 elections.
It's unclear whether he will have to repay the money he earned during his tenure, a decision Mr Turnbull has left to Finance Minister Mathias Cormann.
"(That) is my recollection as the way it's dealt with in the past," he said.
"I'll leave that to be dealt with by him."
The Department of Finance sought to have Bob Day and Rod Culleton pay back their salaries and allowances after the High Court decided they were invalidly elected for constitutional reasons.
They ultimately waived Mr Day's debts and gave Mr Culleton the option to have his waived too.
Senator Ludlam said he didn't have the money to pay back his salaries and allowances.
"It's going to be millions of dollars and my total assets amount to a fast computer and some nice shoes," he told reporters in Perth on Friday.