The Prime Minister says if there is cross-party support to add a fifth flag to the referendum, then he could consider a law change.
The Flag Consideration Panel settled on four flags which will go to a referendum in November, but a campaign for another flag - the Red Peak - has been building.
By late this afternoon, an online petition calling on Mr Key to add the Red Peak design had more than 43,000 signatures, with numbers climbing by the minute.
The Prime Minister has thrown down the gauntlet over the Red Peak flag design, saying if Labour gets on board he could consider changing the law, to allow it to become the fifth option.
At his post-Cabinet news conference, John Key said he would be reluctant to make any change to the line-up because that would be asking him "to jump in front of the process".
"If I drop out one of them, if I drop out one particular flag, there will be a group that will say that was wrong because I was going to vote for that - there will be another group that will say 'I just didn't realise this was a process that could be influenced through social campaign'."
He says while a change was possible, he said one reason for not taking an amendment back to Parliament was the track record of other parties.
"Every time we've gone through this process, political parties have essentially argued publicly that they're supportive and all they've done is for the most part [is] play games after that."
And he singled out the Labour Party.
"If you look at Labour, they've been very disingenuous throughout the whole process so if I've got to go back to Parliament and change the law to have five, are you really telling me they wouldn't then run a campaign that said I'm wasting Parliament's time because I'm now going back to it?
"I mean, these people can play games forever."
Mr Key was asked if he would change his mind, if he had cross-party support for a fifth option.
"Well, they would need to go back and change their position on the flag process, instead of lying to the public and saying they're opposed to this when their policy is actually to change the flag.
"If they want to treat the whole process with respect, they're welcome to come and have a discussion with me, but that is not the way they've played this thing."
Mr Key said there would have to be agreement from the whole Parliament.
"And if Labour want to publicly come out and support the process and the change, that it's an appropriate thing to do and argue that it's an appropriate thing to do... then we might, but that hasn't been what they've done so far."
Labour Party leader Andrew Little said John Key did not need Labour's support to add the Red Peak design to the flag referendum.
He said John Key wanted broad support for purely political reasons, not because he needed it.
"I'm prepared to support what he wants provided he changes the order of the questions in the referendum, providing he makes the first referendum 'Do you want a flag change or not?', and then then if the question is answered positively, then we're going to choose the flag that we want.
"That's what a lot of New Zealanders want, they're telling us they are concerned about the flawed process."
Mr Little said personally he was keen on the Red Peak design.
Mr Key said it was not just about the Red Peak option, it's about the whole process.
"I'm not just going to play games over one thing, if they're going to actually honour their policy and go out there and say, we now support a free vote, we're going to participate, we'll be fully engaged and we'll stop all this mindless bagging, on political grounds, and have a proper debate, then yeah we'll see how it goes."
He said a law change would be required to add the flag to the referendum, and New Zealand First was totally opposed to any law change, so he would not require its support.
Mr Key said if there was broad political support to change the law, then he could consider it.