Mr Hay accused the party of not informing him of a previous conclusion that he would not make a suitable candidate, and said it had strayed from its core values.
"That's why today I've said the Green Party's co-leaders need to step down and step away, we don't want people like this in Parliament, we don't want them in Government, we don't want them in the party,'' he said.
"My leadership bid is not about me, it's not about me being a better leader than Russel Norman. It's because I've completely lost faith in the ability of the party's co-leaders to stick to Green Party kaupapa, to do what the Green Party does, to be fair, transparent, and honest, to do a better type of politics.
"That's been our promise to the people of New Zealand. They've betrayed that promise. They have to go, it is time for them to stand down, they're past their use-by date.''
However, members of the party's executive, co-convenors Georgina Morrison and Peter Huggins, and Auckland co-convenor Vernon Tava, said Mr Hay had "blown out of all proportion'' the decision, which was described as an administrative issue for the party.
Mr Huggins dismissed Mr Hay's calls for the party leaders to stand down saying:
"David's just gone through a process, he didn't get the outcome that he wanted, so he's going to be making statements, but we're clear that we're 100 per cent behind Met and Russel at this point in time.''
Ms Morrison said they were "really disappointed'' in his conduct this week, and didn't rule out "having a conversation'' about expelling him from the party at some point in the future.