ACT Human Rights Minister Tara Cheyne says the government will move a motion in the Assembly calling for the restoration of territories' rights, and wants the opposition to get behind it.

It comes as NT Chief Minister Michael Gunner made a fresh bid to the federal government to allow the territories to make their own laws on the controversial issue.

He has the support of the Country Liberal Party opposition.

Northern Territory and the ACT have been blocked from legalising euthanasia since a 1997 private members bill from Kevin Andrews. In contrast, every state in the country is able to legislate on it.

Voluntary assisted dying is already legal in Victoria and Western Australia, while a bill to allow it is currently before Tasmanian Parliament.

Former Opposition Leader Alistair Coe agreed in a parliamentary motion in 2019 to write to the Prime Minister about territory rights.

His spokeswoman said he penned a letter in February last year, but she would not reveal the contents of the letter or supply a copy.

Ms Cheyne said she had asked Mr Coe on a number of occasions if he had lobbied the Prime Minister about the issue, but she did not receive an answer.

"I'm doubtful that [the letter] ever occurred," she said.

New Liberal leader Elizabeth Lee personally supports the territory having the right to legislate on the matter.

She was one of four Liberals who in 2018 voted alongside Labor and The Greens to rebuke federal senators for voting against a bill that would have restored territories' rights

But the remaining five Liberals did not support the remonstrance motion.

"Ms Lee will consider raising the matter with the Prime Minister and other federal Liberal members, noting that they would already be aware of our view," he spokesman said.

Ms Cheyne says the territory had been hobbled by a lack of leadership from the Liberals in the last Parliamentary term.

She took aim at Mr Coe, and federal senator Zed Seselja, who in 2018 voted against restoring the territories' right to legislate.

"We think the separation of issues is clear and whatever a person's personal position on voluntary assisted dying is, they can still stand up for the territory they are hoping to represent," she said.

"All parties in the ACT should be united when it comes to territory rights, even if we have different party or personal views regarding voluntary assisted dying.

"There is a new opposition leader and new MLAs.

"The Canberra community deserves to know where they stand on voluntary assisted dying given its overwhelming supported by the Canberra community."

Former Liberal leader and senator Gary Humphries said the territory should have the right to legalise euthanasia.

He was a member of the Legislative Assembly when the Andrews Bill banning the territories from legislating on euthanasia was passed

"We took the view at the time very emphatically that the territory was given self governance and it was our responsibility to exercise the powers that entailed," he said.

"I see no reason why it shouldn't be the case now.

"Euthanasia is a state issue, it's an issue where state parliaments have jurisdiction

"There is no logical argument for saying the Commonwealth should play a role in it whatsoever.

"The ACT has the most educated and politically sophisticated electorate in the country, it should have the capacity to make this decision for itself."