Both territories have been unable to determine their own laws on voluntary euthanasia since Federal Parliament in 1997 overturned briefly existing euthanasia laws in the Northern Territory.

The Liberal MP who introduced the legislation, Kevin Andrews, is departing Parliament after losing preselection and now three out of six states - Victoria, Western Australia and Tasmania - now have their own voluntary assisted dying laws and Queensland and South Australia's parliaments will soon debate similar laws.

The member for the ACT federal seat of Fenner is expected on Monday to introduce a motion asking the Morrison government to restore territory rights to determine their own assisted dying laws.

"One of the main arguments that was made in favour of the Andrews' bill was that it was okay to trample on territory rights because no state had passed such laws," Mr Leigh will say, in remarks seen by The Canberra Times.

"This argument was dubious then, but it's plain wrong now.

"The territories aren't advancing ahead of the states - they're being held back."

The family of Canberra man Nebojsa Pavkovic wanted more for him in his dying days.

He died on his 61st birthday in 2016 in palliative care unable to walk and talk after living for more than a decade with Parkinson's disease.

Mr Pavkovic's daughter Katarina Knowles says he was soundly aware inside a body that would no longer work.

In the end, Mr Pavkovic communicated by squeezing the hands of any family members, doctors and nurses.

"He was really truly bedridden and it was just the worst," Ms Knowles said.

"He was so cognitively present the entire time, and it was just difficult because he wouldn't be able to communicate so often people would mistake him for not being cognitively present and perhaps simplifying things when really he was 100 per cent across it."

In a decision she calls hard but also the "most amazing thing that any person could do", Ms Knowles says her father expressed the intention to end his life. She said he stated this clearly and several times to her and her mother.

While in hospital, he refused food through a feeding tube - a process which took five weeks to reach its end.

"On his last day, just before he passed away, you know I said 'happy birthday' to him. Do you want some more pain medication?" she said.

"He squeezed my hand and then that was, the last time that I interacted with him."

While the family had support, she says her father's death could have been better.

"If we had had the option, then a lot of things could have been a lot easier," Ms Knowles said.

"And also, you never know when you're in palliative care, you know, every day you're not sure if you should say I'll see it tomorrow or not because, you know, who knows what would happen.

"So I think the option definitely would have been appreciated and at least it would have made the end a little less traumatic, I suppose, is the key there."

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Andrew Leigh says Ms Knowles is not the only Canberran who would like options when it comes to end of life decisions.

"Last Wednesday, I held a telephone town hall, with hundreds of people from my electorate. As part of the event, we did a short survey about euthanasia and territory rights," the MP will tell Parliament.

"More than four-fifths supported voluntary assisted dying, and an even higher share wanted territories to have the right to legislate on the issue. It's past time we scrapped the undemocratic ban on the ACT and NT legislating about euthanasia."

Calling the Andrews' bill "anachronistic," Mr Leigh and insists restoring territory rights is not about directing them to consider making laws relating to euthanasia, rather he says this is about allowing them to consider such laws if they want to.

Mr Leigh last tried to repeal the ban on the territories making laws on euthanasia in 2018 with a co-sponsored private members bill with fellow Labor MP Luke Gosling.

A spokesman for Attorney-General Michaelia Cash says the government has no plans to change laws affecting voluntary euthanasia, but it recognises that people have strong views about dying with dignity, and with minimal pain.

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