Mr Barr has also promised to raise the territory's grievances with Prime Minister Scott Morrison directly, after the federal government failed to respond to multiple letters from the ACT expressing its concern and frustration about the decades-long ban.

ACT Human Rights Minister Tara Cheyne last week sent her third letter on the issue in the past six months to the federal government, after the first two went unanswered.

The ACT is becoming increasingly frustrated with the Morrison government's refusal to engage with its calls to have the so-called Andrews Bill repealed in Federal Parliament.

Scrapping those laws would restore the rights of the ACT and NT parliament to pass - or reject - their own assisted dying legislation.

In her most recent letter, sent to federal Attorney-General Michaelia Cash, Ms Cheyne said allowing the two territories to make their own legislation on the contentious subject should not controversial.

NSW is now the only state which hasn't passed assisted dying legislation, although a bill is expected to be presented to its parliament next month.

Asked on Monday about the federal government's snub, Mr Barr said he would raise the matter directly with Mr Morrison.

MORE OUR RIGHT TO DECIDE CAMPAIGN:

And in a warning to the Coalition and its local Senator Zed Seselja, who staunchly opposes a repeal of the Andrews Bill, Mr Barr said territory rights would be turned into a campaign issue ahead of the next federal election.

The next election is due before May next year.

The overwhelming majority of people in Australia and in Canberra support the rights of the ACT and NT to decide their own voluntary euthanasia laws, according to polling commissioned by progressive think tank The Australia Institute.

The Canberra Times has since late July been calling for the Andrews Bill to be repealed through its Our Right to Decide campaign.

A parliamentary inquiry is currently examining a bill drafted by Country Liberal Senator Sam McMahon, which would restore the rights of the NT, but not the ACT, to legislate on assisted dying.

A number of legal experts have called for the ACT to be added to the bill to avoid creating a fresh layer of discrimination against Canberrans.

The inquiry has also received submissions from opponents of the McMahon Bill, who fear opening the door to voluntary assisted dying would disproportionately harm vulnerable groups.

The Canberra Times has contacted Senator Cash for comment.

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