Prime Minister John Key says he doesn't see gay marriage as a top priority, but he will support legislation overhauling the Marriage Act at its first reading.

Mr Key last week said he was not opposed to same-sex marriage after US President Barack Obama expressed his support on the issue.

Labour MP Louisa Wall is drafting a private members' bill to legalise same-sex marriage - and, if it's pulled from the ballot and makes it onto parliament's order paper, Mr Key says he will support it to at least its select committee stage so it gets a chance to be debated.

Asked what issues he wanted teased out, Mr Key said: "Let's just have that debate".

"As I've said, personally I'm not opposed to gay marriage but, you know, it's an issue that the government wouldn't put on the agenda today because we don't think it's a top priority issue," Mr Key said.

"But if a member wants to put a bill in, then we can't or obviously wouldn't stop that process and I'm more than happy for that debate to be aired through a select committee process."

Mr Key says his government is more focused on economic issues than "conscience moral issues".

"These are difficult economic times, there are big challenges for the government, and we need to use our precious time in parliament really to resolve those issues.

"We accept this is an issue for a small group of New Zealanders and, as I say, if it comes up through the members' process, we'll back that but in terms of government house time, we have bigger priorities."

He has previously said he believes civil unions between same-sex couples, which have been allowed in New Zealand since 2005, were enough.

Labour leader David Shearer says he personally supported marriage equality, while the Green Party has confirmed all of its MPs will support gay marriage legislation.