THE Greens plan to push Premier-elect Will Hodgman for a fair share of resources and parliamentary rights.
Greens leader Nick McKim said he would seek a meeting with Mr Hodgman next week after the minor party failed to win enough seats to qualify for party status in the Parliament.
Mr McKim said he expected "some shrinkage" in what the Greens received after their numbers in the lower house were slashed from five to three in the election.
"What we believe is fair is a pro rata arrangement," Mr McKim said.
"So, three-fifths of what we previously received in terms of resourcing and the same ... in terms of parliamentary rights."
Allocation of any extra resources beyond the basic entitlements of backbenchers is now up to the new Liberal government.
Their parliamentary question and speaking time privileges will also be determined by the Hodgman government.
Incoming treasurer Peter Gutwein said yesterday that Mr Hodgman would consider any proposal from the Greens' leader.
"But at the end of the day I think Mr McKim has to accept that the Tasmanian people have spoken and judged the Greens and Labor very harshly," Mr Gutwein said.
On Thursday Mr Hodgman said he would stick to the law and would not give his opponents any special treatment.
The Liberals yesterday would not be drawn on which law or laws Mr Hodgman was referring to.
Mr McKim said there were no laws determining how resources were distributed.
"The Premier shouldn't be trying to invent mythical laws that don't exist in order to dodge responsibilities," Mr McKim said.
"He has responsibility for this decision and he needs to accept that."
Mr McKim said it was important for democracy that opposition and cross-bench MPs were resourced to an adequate level and had the capacity to hold the government to account.