The Labour Party will table a bill in Parliament to include the Red Peak design as well as a 'yes'/'no' question in the first flag referendum.
Labour leader Andrew Little said his party would table the bill this week.
"John Key has responded to public pressure over the final flags chosen - now it's time to also hear those who want to vote 'no' in the first referendum.
"Labour's bill, which we will seek cross-party support for this week, will provide a meaningful referendum that all New Zealanders can have confidence in.
"Whether you want to keep the current flag, vote for Red Peak, a fern or the koru, this bill will allow all views to be heard.
"Then, if more than half the country votes for some kind of change, the second referendum will put the winning new design up against the current New Zealand flag."
Mr Little said New Zealanders did not want two referendums at an enormous cost, and Mr Key had misread public sentiment.
"He's now understood that - the way things are going - New Zealanders are likely to default to the present flag at the cost of $26 million."
Mr Key said he was happy to change the law to include the fifth flag - but only if Labour played the game.
"But actually Labour don't. They want to play politics with it," he said.
"It's quite tragic really because they privately go and tell people they support the change [of] the flag. They don't do it because they just try and turn it into a political football."
Mr Key said he would not support Labour's bill to include a 'yes'/'no' question in the first referendum.
"How can you have a 'yes'/'no' vote when people don't know what they'd be voting for?"
'Right side of history'
The Flag Consideration Panel settled on four flags to go to a referendum in November, but the campaign for Red Peak as a fifth flag has been building.
Nelson-based venture capitalist Rowan Simpson, who has played a key role in the online campaign supporting Red Peak, told Morning Report both parties needed to think about giving people choice.
"I think there's a real opportunity for either or both of them to be on the right side of history with this. I think at the moment they seem to be determined to do the opposite," he said.
"This is not a left-wing or a right-wing movement. It's just New Zealanders saying 'we'd love to have the choice to vote for this flag that we like'."