New Zealand's Labour Party says there is no reason the Government should not support the Marshall Islands lawsuit against the nine countries with nuclear weapons.
The Marshall Islands government is suing the United States and the eight other nuclear-armed countries for failing their obligations to disarm
It is filing the lawsuits in the International Court of Justice and the US Federal District Court.
The United States says it is examining those lawsuits.
In the 1970s, New Zealand took France to court in a bid to stop nuclear weapons tests at Mururoa Atoll and at other sites in the South Pacific.
The Marshall Islands has accused the nuclear powers of failing in their obligation to negotiate nuclear disarmament.
The US State Department has defended the US record, saying its stockpile of nuclear weapons has been cut by 80 percent since the Nuclear Non-Proliferation Treaty took effect in 1970.
The Marshall Islands filed the lawsuit against the US in the US because the US refuses to recognise the International Court of Justice.
The other cases have been lodged with the ICJ in The Hague.
In the 1970s, New Zealand took France to court in a bid to stop nuclear weapons tests in the South Pacific.
The Labour Party's disarmament spokesperson, Maryan Street, says she will be asking the foreign minister to support the suits.
"Here is a fundamental and critical issue that our government can take some leadership on,'' sh sayd.
"Anybody who stands up for a case in front of the International Court of Justice should not find diplomatic barriers in their way, because it is justice."