The Australian Capital Territory and the Northern Territory may soon wrestle back control of their euthanasia laws — more than two decades after the NT's landmark legalisation of the practice was voided by the Commonwealth.

A motion put forward by Liberal Democrats senator David Leyonhjelm, which could see the territory governments rather than the federal government legislate on the issue in their jurisdictions, passed today.

In 1995, the Northern Territory famously became the first Australian jurisdiction to legalise euthanasia.

But that was effectively voided two years later when the federal government passed a bill that banned the ACT and NT from legalising assisted suicide.

It remains in place, despite Victoria passing its voluntary euthanasia law in October 2017, and the NT Chief Minister Michael Gunner urging Prime Minister Malcolm Turnbull to "alter" his Government's position on the issue.

"As a result the states all have their own authority to debate and introduce assisted suicide if they wish … but because of this [federal] bill the Northern Territory and the ACT are prevented from doing it," Mr Leyonhjelm said.

"My bill addresses two issues: territory rights, and the right to die. I am a firm believer in both."

David Leyonhjelm's bill could eventually see the NT and ACT regain the right to legislate on assisted dying. ( AAP: Lukas Coch )

Support for euthanasia 'overwhelming'

The passing of Mr Leyonhjelm's motion today will now see his Restoring Territory Rights (Assisted Suicide Legislation) bill debated in the Senate in August, followed by a free vote.

If successful, it is likely to then progress to the House of Representatives for another debate and vote.

Earlier today, he told the ABC he believed it would pass easily, with support from a number of Greens, Labor and Crossbench senators, as well as Northern Territory Nationals senator Nigel Scullion.

But he also said although the upcoming Senate debate should centre on which level of government had the right to legislate on the issue, some senators' views may be clouded by their personal stance on euthanasia.

However, this could also work to his benefit.

"There could well be people who will vote for it because they don't think the Federal Government should be telling the territories what they should do on this issue," he said.

"But then if it came to a vote in the territory and they were in a position to influence it they would say 'vote no'.

Liberal senator against law change

Asked why he — a New South Wales senator — was preoccupied with territory rights, he said he was more motivated by the Federal Government's "overreach" when it came to legislating euthanasia laws.

"It's not about the Northern Territory, it is about assisted suicide. I don't think the Government should take on the authority or the power to tell people that you can't die," he said.

"I regard that as total government overreach."

While he said the bill would not automatically make assisted suicide legal in the territories, it would at least remove a "nonsensical law based on the tenet that some Australians are entitled to more democracy than others".

But earlier today, Liberal senator Eric Abetz said he was concerned by the idea, saying it was counterproductive as taxpayers were spending "millions of dollars on mental health and suicide prevention".

He also claimed territory parliaments had "not been able to demonstrate why they should be permitted this power".

"For the parliament to permit and promote suicide in any circumstances fundamentally diminishes the value we place on each individual human life," Senator Abetz said.

"In the 20 years since the Andrews Bill passed the parliament, the territory parliaments have not been able to demonstrate why they should be permitted this power.

"I also note that neither parliament has an upper house nor has successfully mounted a case to their people for self-government.

"Given the strong opposition from Labor elders, including Paul Keating, I am hopeful that all sides of politics will work to ensure that such a bill is not rushed on in the next sitting weeks."