The ACT's opposition leader said she would continue to lobby her federal colleagues, including Senator Zed Seselja, to to restore territory rights.
It comes as the ACT could be left out of a renewed attempt to overturn a bill that bans the territories from making laws on euthanasia.
Northern Territory Country Liberal Senator Sam McMahon will put forward a private members' bill to restore territory rights.
But the bill would only include the Northern Territory, after Senator McMahon said Senator Seselja would not support it.
Senator Seselja's position puts him at odds with the Canberra Liberals, after ACT Opposition Leader Elizabeth Lee co-signed a motion earlier this year in the ACT Legislative Assembly that called for the federal government to bring forward a bill to remove the law by the end of the year.
ACT Human Rights Minister Tara Cheyne accused Senator Seselja of undermining Ms Lee.
"Elizabeth Lee and the local Canberra Liberals united with ACT Labor and the ACT Greens in March to lobby the federal parliament on restoring territory rights," Ms Cheyne said.
"By asking NT Senator Sam McMahon to leave the ACT out of her prospective bill to restore territory rights, Zed has not only abandoned Canberrans but he's gone against his own colleagues' wishes and actively and knowingly undermined the ACT opposition leader."
Ms Lee said the Canberra Liberals' position on the matter was clear and said she would continue to discuss the matter with her federal counterparts.
"I have made the views of the Canberra Liberals' Legislative Assembly team very clear to Senator Seselja and will continue to discuss this matter with him and other federal colleagues," she said.
"The ACT Legislative Assembly is democratically elected by the people of Canberra. It 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."
The territories have had no ability to make legislation on voluntary assisted dying since the so-called Andrews bill passed 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.
Senator Seselja has strong views against euthanasia and has not supported previous attempts to overturn the 24-year-ban.
A spokeswoman for Senator Seselja said these views had not changed.
"The senator's views on euthanasia are well-known and have not changed," she said.
"Individual senators are free to present legislation to the parliament as they see fit."
ACT Senator Katy Gallagher on Monday said Senator Seselja was the biggest barrier for the territory to gain the right to legislate on the issue.
Senator Gallagher wrote to Senator Seselja in March, urging him to support moves to restore territory rights and even asked him to co-sponsor a bill. She wrote to him again in May.
But Senator Gallagher has yet to receive a response.
Senator McMahon's bill would be the latest in a series of attempts to overturn the ban.
Most recently, federal Labor member for Fenner Andrew Leigh introduced a motion calling for territory rights to be restored.
In 2018, former senator David Leyonhjelm put forward a bill to restore rights. The bill went to a vote in the senate where it failed by only two votes.
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