Internal tensions in the Greens have escalated further with the party's former leader Christine Milne challenging two NSW MPs to condemn members of the party calling for a split in the movement.

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.

Christine Milne has called for members advocating a split to stand down. Credit:Alex Ellinghausen

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.