Prime Minister John Key says he will not rule out backing the gay marriage bill all the way, instead of just through its first vote in Parliament as he originally said.
This comes as a pro-gay marriage group says ultimately it is aiming to have multiple-partner marriages made legal.
The controversial legislation was drawn from the members' ballot last week and will be decided by a conscience vote.
Mr Key says he is telling his MPs that if they are unlikely to vote the bill into law after a third reading, then they should not vote for it at its first reading.
He also signalled he may follow through with his support beyond the first reading.
Earlier an anti-gay marriage website came under fire from computer hackers and an American pop group wanting to disassociate itself from the campaign.
Christian lobby group Family First launched its website at the weekend.
Since then the band, Train, has said it will ask the group to remove a link to its song Marry Me from the website.
The site was also off-line on Monday afternoon after it was attacked by hackers.
Family First's national director Bob McCoskrie says the computer hacking was an unfair attack on the debate.
Mr McCoskrie would not be drawn on who he thinks launched the hacking attack on his website.
