Fairfax Media last month reported on the formation of a new factional grouping within the Greens calling itself "Left Renewal" and advocating a radical platform rejecting the legitimacy of the state and calling for the end of capitalism.

That development has been followed by some Greens members calling for the development of a left-wing alternative to the party. Deputy membership officer, Tomas Hamilton, last week called the Greens a "hollow shell" and advocated forming "a proper anti-establishment left populist party".

Ms Milne, who resigned as the Greens' federal leader in 2015, called on two prominent left-wing Greens MPs from NSW to condemn those remarks and for Mr Hamilton to resign.

"These individuals identify with [federal senator] Lee Rhiannon and [state MP] David Shoebridge," Ms Milne said. "They must be confident they have their support. That really puts the onus on those MPs to call them out.

"Seeing an elected office bearer say that they're intending to develop a base for a new party is completely destructive. They should leave now."

Ms Rhiannon and Mr Shoebridge have said they are not Left Renewal members but have defended its members' rights to express their views.

"I don't think the expulsion of Greens members from Left Renewal or the right-wing grouping is a sensible way forward," Ms Rhiannon said. "We need to remain an inclusive party that considers a diversity of views consistent with our four Greens principles."

Ms Rhiannon said the party should use democratic forums to discuss policy proposals.

But Mr Hamilton, a critic of some conservative members of the NSW party, denied he was of the Left Renewal faction and said he should not resign for expressing dissenting views.

Young Greens members of Left Renewal have publicly expressed similar sentiments about developing an alternative to the Greens.

Mr Shoebridge said he was unable to respond because he was on holiday and had not seen Mr Hamilton's remarks.

Ms Milne also partly backed calls from her predecessor, Bob Brown, who called on Ms Rhiannon to move on from politics.

"Lee was democratically elected a year ago but I do think she should think about not running [for another term]," Ms Milne said. "If you're going to call for renewal then you have to lead."

Ms Rhiannon rejected calls by Mr Brown to stand down after last year's election, saying she intended to continue in her job.

The recent divisions represents the escalation of an old battle between the party's left wing, known to detractors as the "Eastern bloc" and more centrist MPs, a group dismissed by opponents as "tree Tories".

Candidates backed by the left have lost out in the two most recent state preselections in NSW.