Andrew Leigh, who represents the ACT seat of Fenner, and Luke Gosling, who holds the Northern Territory seat of Solomon, will co-sponsor a private members bill to repeal the ban on the territories making laws on euthanasia.

Mr Gosling is against euthanasia, while Mr Leigh supports it.

However Mr Leigh said he, Mr Gosling and the rest of the Labor party believed the territories should have the right to choose whether they legalised voluntary assisted dying.

"I don't think it's any logical contradiction having one position on the substantive issue but believing the powers of the parliaments should be expanded," Mr Leigh said.

"The ACT Legislative Assembly is just as mature as any state parliament. Queensland's parliament was unicameral the last time I checked and no one is taking away their rights."

Mr Leigh is hopeful the bill will be debated next week.

It's likely to appear on the notice paper on Monday, although if Prime Minister Malcolm Turnbull doesn't grant leave for debate, the majority of the house would have to vote to suspend standing orders for debate to occur.

That could be problematic, because even if Labor got the crossbench on board, two Coalition MPs would have to cross the floor to allow the house to debate the bill.

Mr Turnbull is under pressure to stop another private members bill on euthanasia reaching the lower house.

The Senate is currently debating Liberal Democrats Senator David Leyonhjelm's bill to dismantle the restrictions on the territories.

Senator Leyonhjelm struck a deal with Mr Turnbull in 2016 that cleared the way for the Senate vote to take place, however Mr Turnbull has said in recent days that arrangement did not extend to the House of Representatives.

A vote on the Leyonhjlem bill is expected on Tuesday, with a long list of speakers on Monday night.

A growing number of Coalition senators have indicated support for restoring territory rights, including education minister Simon Birmingham, Ian McDonald, Steve Martin and Nigel Scullion, who is the Liberal senator for the Northern Territory.

ACT Labor Senator David Smith will help pass the Leyonhjelm bill even though he told The Guardian he has "grave reservations" about voluntary euthanasia.

ACT Liberal Senator Zed Seselja will vote against it as he believes the issue of euthanasia and territory rights cannot be separated.

"Make no mistake, this is not about territory rights, it’s about human rights. I fear the passage of Senator Leyonhjelm’s Bill will lead to assisted suicide becoming legal in the ACT under a regime that will have minimal safeguards," Mr Seselja wrote in an opinion piece for The Canberra Times.

However Canberra Labor MP Gai Brodtmann struck out at Senator Seselja's decision on ABC Radio on Tuesday morning.

"I don't know what will play out after this week but I do want to remind Senator Zed Seselja that he is a territorian and he represents the people of the ACT," Ms Brodtmann said.

"This is a question of territory rights, this is question of equality and of the right of the people of the ACT and the Northern Territory to enjoy the same rights as those in South Australia, Victoria, Queensland and South Australia and Tasmania. In 2018, in a democracy that's only fair."

Meanwhile ACT politicians attended a rally at Parliament House on Tuesday morning ahead of the Senate debate.

ACT Greens crossbencher Caroline Le Couteur said the people of Canberra were sick of being treated as second class citizens.

"The ACT was granted self-government almost 30 years ago. It’s absurd that Canberrans should still be prevented from determining our own laws, and be subjected to these undemocratic and discriminatory restrictions," Ms Le Couteur said.

ACT Labor backbencher Tara Cheyne said removing the restrictions would not mean the territory government would move immediately to legalise euthanasia.

"What it would do is simply give our citizens and our parliament the same right to decide for ourselves as those Australians living in the states," Ms Cheyne said.