In a rare show of consensus, the House of Assembly on Wednesday supported a Greens' motion to allow the Aboriginal flag to be flown when the Tasmanian flag is flown and not just during NAIDOC week.

The Legislative Council will now vote on the motion.

Mr Mansell said he supported local councils flying the Aboriginal flag but not the Parliament.

"There is a big difference with flying the Aboriginal flag at the seat of power and in local government who are acknowledging Aboriginal people," he said.

"The difference is Parliament House is a place that has sidelined the Aboriginal people and decides our fate and rights.

"Local councils are not in the same boat.

"If the seat of power wants to fly the Aboriginal flag they have to earn that right."

Mr Mansell believes Parliament is largely ignoring Aboriginal people.

"The people in the Parliament do not worry about Aboriginal disempowerment or addressing injustices and that's not good enough," he said.

"We are still waiting to have Aboriginal representation in Parliament, a treaty with our people and the return of stolen lands."

Mr Mansell has long argued for two designated seats for Aborigines in the Tasmanian Parliament.

During the debate on the flag flying motion, Greens leader Cassy O'Connor repeated calls for a new date for Australia Day and the renaming of the Batman Bridge in Launceston.

"John Batman hunted and killed dozens of Aborigines yet there is a bridge named after him," Ms O'Connor said.

Labor member for Bass, Jennifer Houston, an Aborigine, broke down and wept as she spoke of the deaths of Aborigines ahead of NAIDOC Week this week.

She said the week's theme, 'Always was, always will be', recognised the importance of connection with the community and Aboriginal lore.