Turmoil is continuing among the Greens over the decision to block inflation-based increases to fuel tax, with NSW branch members calling on the party's national council to intervene.

A group of NSW Greens is pushing the party's national arm to demand the party room reverse its decision not to support the Abbott government's plan to restore the indexation of fuel excise.

A motion will be put to a national council meeting this month and comes after NSW branch members advocated a change in the party's position on Saturday.

One party source said that if restoration of fuel excise was not put to the Senate during this sitting of Parliament, the NSW party could use its August meeting to compel NSW senator Lee Rhiannon to cross the floor and vote in favour of the fuel tax hike.

In a sign of the intense divisions over the issue, Senator Rhiannon invited members to have their say at Saturday's meeting, even though the policy has been finalised, setting up a situation in which the party room has one policy and the membership another.