Tara Cheyne said a proposed push to overturn the ban from Northern Territory Country Liberal Senator Sam McMahon, which leaves out the ACT, was unlikely to gain traction.

Instead, Ms Cheyne said a federal government minister needed to lead the cause as it would be more likely to be debated.

"The simplest, most straightforward and least costly way to resolve the issue of territory rights is for a legislative amendment to be put to the federal parliament, debated and passed. Ideally a federal government minister would lead this," Ms Cheyne said.

"Historically, several senators and members have introduced a bill to restore territory rights but few have been debated - because the federal government did not bring them on.

"A federal minister leading this work would mean it would form part of the government's legislation program and thus be debated."

In a 2018 senate vote on a bill to overturn the ban, only two federal ministers - Simon Birmingham and Marise Payne - voted in favour of the repeal.

The territories have not had the right to legislate on euthanasia since 1997, due to a bill spearheaded by Liberal Kevin Andrews. The bill was introduced in response to the NT passing the laws to allow it in 1995.

Earlier this year, the ACT and the NT joined forces to campaign for the federal government to repeal laws that block them from making legislation on the controversial issue.

But more than four months later, there has been silence from the federal government.

Ms Cheyne and the Northern Territory Attorney-General Selena Uibo wrote a joint letter in March to three Commonwealth ministers calling for action on a bill, accusing the government of breaching international rights.

However, two of the three ministers - former attorney-general Christian Porter and former deputy prime minister Michael McCormack - have since changed.

In an opinion piece published in The Canberra Times on Saturday, Ms Cheyne and Ms Uibo described the ban as "an assault on territory citizens' democratic rights".

"While we've waited for a response, individuals and families have been devastated by the inability to make decisions about their own lives," the opinion piece said.

"The ACT and NT governments remain firmly united on this senseless situation needing to be resolved for our citizens as a priority. Enough is enough."

Earlier this year, Ms Cheyne indicated she was prepared to take the matter to the United Nations if the federal government did not take steps to remove the law.

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When asked this week whether this was still on the table, Ms Cheyne said it would be dependent on the federal government's response.

"The response we receive may influence how we continue to pursue this issue," she said.

The renewed push from Senator McMahon leaves out the ACT, as her coalition colleague, ACT Senator Zed Seselja, would not support the bill.

Senator Seselja, who is a minister for international development in the Pacific, is a staunch opponent of voluntary assisted dying.

The territories could soon be the only two jurisdictions where voluntary assisted dying is not legalised.

South Australia is the most recent state to legalise voluntary assisted dying. It is the fourth state to pass legislation; joining Tasmania, Western Australia and Victoria.

Queensland has also recently introduced legislation to its parliament, which is expected to be debated in September. A bill is also expected to be introduced to the NSW Parliament in August.

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