Green Party MPs have held a crisis meeting at Parliament as they debate suspending two of their MPs from the party's caucus.
The party's other co-leader, James Shaw, said he and Mrs Turei felt betrayed by the two MPs and he would seek to suspend them both.
Dr Graham is ranked eighth on the party's list and Mr Clendon is at 16th.
On his way into this morning's meeting, Mr Clendon rejected comments by the party's general manager, Sarah Helm, that he and Dr Graham were disgruntled MPs and that they were grandstanding.
"I think it's unfortunate that Sarah told untruths, what she said online was simply not true, I've responded to that, and I'm disappointed that a senior party employee should resort to telling basically lies."
Dr Graham said he had not talked to Mr Clendon yet this morning, and it was up to the party to decide what happened next.
"I think it's quite important not to enflame things any further. I think we need to be cool and calm and dignified and have a decent discussion."
While MPs remain ensconced in the Bowen House offices, the party sought to clarify that the initial meeting had ended and the regular caucus meeting was now under way.
Green Party MP Barry Coates said he fully backed Mrs Turei staying on as co-leader, saying it was a shame Dr Graham and Mr Clendon have acted the way they have.
"The way that they have decided to withdraw from the party is incompatible with the way that the Green Party does [things]. The first thing I heard was from from a Radio New Zealand report, and that's not the way we do things in the Green Party."
His colleagues, Catherine Delahunty and Marama Davidson, said they too were 100 percent behind Mrs Turei.
Ms Delahunty said Dr Graham and Mr Clendon had the right to do what they thought was right, but she did not agree with how they had gone about it.
"The way that they have gone about it has not made us very happy and I don't agree with it either. I don't support any view that our co-leader has been anything other than courageous about her past and honest about who she represents.
"This Parliament should be a parliament of representatives. Metiria has been a wonderful MP for 15 years and other people while in office have done things that are less than perfect, but they are not being thrown under the bus by anyone - I stand with Metiria."
Mrs Turei has admitted lying to Work and Income during the 1990s while on a benefit] and enrolling in an electorate she did not live in, in 1993.
'Unilateral and deliberate attempt to damage'
Former Green Party co-leader Jeanette Fitzsimons, who led the party for 14 years from 1995, said it was a sad seeing this kind of behaviour against the party from her "old friends" and colleagues.
"[Kennedy Graham and David Clendon have] put their personal feelings about personal morality ahead of the desperate need for policies that the Greens bring," she told Nine to Noon.
"They've not only dumped on the team that they're part of ... but on the country which needs action on climate change, poverty, clean water and many other issues."
But Ms Fitzsimons would not support the actions of Mrs Turei, in registering on the electoral roll using the wrong address.
"My personal conscience does not support making a false claim about what electorate you live in for voting purposes, so I don't support that Metiria did that.
"But nor do I think that a misdemeanour like that ... 25 years ago when she was really young and before she had anything to do with the Green Party - I do not see that as reason for standing down."
She said the caucus would have no choice but to suspend the two MPs.
"This is a unilateral and deliberate attempt to damage and while it's very sad, and I would hate to do that to two of my old friends, I think I would."
Mr Shaw said he would also ask for the two MPs to be expelled from the party altogether.
Ms Fitzsimons said that appeared to be the "cleanest way to handle it from his point of view", and that this matter had to be resolved ahead of the election.
Fellow former MP Sue Bradford told Morning Report she backed the co-leaders' push to suspend the two MPs.
"It's really outstanding to see that the leadership of the caucus have not been afraid to come out this time and say, 'actually, we've had enough, these two are not doing the job that they're being paid to do, that the party put them there to do - and on top of that they're undermining their leader and undermining the courageous stance she's taken'."