Labor MPs made the plea as backbenchers Luke Gosling and Alicia Payne introduced a private members' bill to repeal the John Howard-era laws that prevent territory parliaments from making their own assisted-dying laws.

Opponents are already starting to mobilise, with Liberal MP Andrew Wallace urging his colleagues to stand up for the "sanctity of life".

After numerous failed attempts to overturn the so-called Andrews bill in the past two decades, the latest push represents the best chance of ending a ban that critics argue has turned ACT and Northern Territory residents into "second-class citizens".

"This is a significant day," said ACT Chief Minister Andrew Barr, who was seated in the public gallery when the bill was introduced on Monday morning.

"It is a day we've encountered before, but this time is different."

Labor MPs are trying to frame the bill as a matter of restoring democratic rights, hoping to avoid it becoming a proxy for a debate on the far more contentious subject of voluntary assisted dying.

Seven Labor senators voted against David Leyonhjelm's bill to restore territory rights in 2018, due to their personal opposition to assisted dying.

With the Albanese government to grant its members a conscience vote, Labor parliamentarians could again play a role in sinking a bill that is likely to be opposed by the overwhelming majority of Coalition members.

Mr Gosling, who is personally opposed to voluntary assisted dying, defended the rights of his colleagues to vote according to their conscience.

But he appealed for them to treat the bill as an issue of restoring democratic rights.

"That [legalising assisted dying] is not what is at stake here. They are issues for the legislative assemblies to consult on, to debate and to decide."

In a message to politicians on all sides, Ms Payne insisted the debate wasn't about the pros or cons of voluntary assisted dying.

"This is not about an individual's views on voluntary assisted dying. It's about giving rights to Australians that don't have those democratic rights right now," she said.

All five territory MPs - including the ACT's David Smith and Andrew Leigh - spoke in support of the bill in the House of Representatives on Monday afternoon.

Mr Wallace and fellow Coalition MPs Luke Howarth and Terry Young declared their opposition to the bill, while Bass MP Bridget Archer revealed she would support it.

"We have a chance to deliver the territories what is rightly theirs," Ms Archer said.

Mr Young argued the territories shouldn't be allowed to debate the subject because their parliaments did not have upper houses, even though his home state of Queensland doesn't have one either and it still passed assisted dying laws.

Mr Wallace, a former speaker, said the bill presented a chance for MPs who believed in the sanctity of life to "defend that right".

"If we give that up today, this week, however long this debate takes, it is gone forever," Mr Wallace said.

Mr Gosling revealed he had written to new Country Liberal senator Jacinta Nampijinpa Price, who is the only territory senator yet to pledge their support for overturning the Andrews bill.

Senator Price has been contacted for comment.

The Canberra Times has for the past year been calling for the Andrews bill to be repealed as part of its Our Right to Decide campaign.