Malcolm Turnbull says the High Court has enough on its docket not to deal with the case of Labor senator Katy Gallagher.
Questions have arisen about the ACT Labor senator's eligibility to remain in parliament.
Senator Gallagher's mother was born in Ecuador in 1943 to British parents, potentially making her a citizen by descent.
However, she says the issue was investigated as part of the Labor candidate vetting process and it was determined she had not obtained Ecuadorian citizenship by descent from her mother.
The High Court is examining the dual citizenship of five members of parliament and another two are due to be referred to the court next week.
"I think the High Court has got plenty of citizenship test cases already on its docket," Mr Turnbull told reporters in Sydney on Wednesday, when asked about the Labor senator.
The prime minister said he would leave it to Labor leader Bill Shorten.
Constitutional law expert Professor George Williams said Senator Gallagher appeared not to fit into the category of being "entitled" to foreign citizenship.
"What's become clear from people who are experts in Ecuadorian law, of which I'm certainly not one, is to become an Ecuadorian citizen you need not only to fit within the birth of your parent, grandparent or great-grandparent, but also you need to actually take an active step," he said.
He said the already-running court cases would provide a clearer picture on whether MPs in Senator Gallagher's position were ineligible.
