In a rare tripartisan motion, members from the ACT Legislative Assembly across the three parties called on the federal Parliament to bring forward a bill to remove the law by the end of the year.

Ms Cheyne said if the federal government did not remove the law she would consider elevating the matter "potentially onto an international stage".

When asked if this meant she would take the matter to the UN, Ms Cheyne replied: "it's not off the table".

The ACT and Northern Territory governments have previously accused the federal government of breaching international laws on the matter in a joint letter penned earlier this month.

The territories have had no ability to make legislation on voluntary assisted dying since the so-called Andrews Bill passed in the federal parliament in 1997.

The bill was introduced by Liberal MP Kevin Andrews in response to the Northern Territory passing laws to allow it in 1995.

Ms Cheyne's comments came after the Assembly joined together on Wednesday morning to call on the federal government to restore the territories' rights to make laws on euthanasia.

Several members of the assembly spoke about their feelings towards the laws. Ms Cheyne said it meant people in Queanbeyan had greater rights.

"It's one thing to not support voluntary assisted dying ... I accept and acknowledge that there are some who don't and won't ever support voluntary assisted dying," she said.

"But what I can't accept is a view that supports Australian citizens having different democratic rights in their own country by virtue of where they live.

"Someone who is 15 minutes away across the border in Queanbeyan for example has more rights than any other citizen who lives in the ACT."

Greens backbencher Johnathan Davis echoed the sentiment.

"The number one thing you enjoy in Queanbeyan that you don't enjoy if you live in the ACT is full and uninhibited democratic rights," he said.

"Your representatives are hamstrung, unable to represent you, you ambitions, your hopes, your dreams and the policy positions you support at the ballot box once every four years, we are in effect less powerful, less influential, less able to service than our NSW state counterparts."

Opposition Leader Elizabeth Lee said the ACT government should have the right to legislate on the matter.

"We should have the right to legislate on this matter on behalf of Canberrans just as we have the right to legislate on a whole host of other matters dealt with by state and local governments across Australia," she said.

The original motion was co-signed by Ms Cheyne, Ms Lee and Attorney-General Shane Rattenbury.

Other members of the Assembly were invited to co-sign the motion. All Labor and Greens members signed the motion but Ms Lee signed the motion on behalf of all Liberal MLAs.

She said the Liberals had made a collective decision that she would sign the petition on behalf of the party.

"I will be signing the letter on behalf of the Canberra Liberals," she said.

"That is our party position."

But the Canberra Liberals allow a conscience vote on euthanasia.

Ms Lee was one of four ACT Liberal MLAs who voted alongside Labor and the Greens to rebuke federal senators who voted against a bill to restore territories' right in 2018.

The Opposition Leader recently wrote to Prime Minister Scott Morrison to let the ACT make euthanasia laws.

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