Ms Cheyne said she had been given a card left by the Canberrans to their loved ones who decided to take their own lives, apologising for not informing them of their plans.

"You could have been put in a difficult position with police if you had known," the note read.

ACT and the NT are barred from legalising euthanasia and would need Federal Parliament to remove sections of the Self Government Act to be able to do so.

Chief Minister Andrew Barr penned a letter to Prime Minister Scott Morrison on Wednesday urging action to give the territory the right to legalise voluntary assisted dying.

Opposition Leader Alistair Coe said he would write to the Prime Minister in the near future about territory's right to legislate on the matter.

Ms Cheyne said she had come across paternalistic opposition from some federal MPs who believed the ACT needed protecting from itself.

"Canberrans are already suffering due to the federal legislation in place," she said.

"The card is such an eloquent and tragic illustration of this. This is a Canberra couple who died without letting friends or family know until after the fact because they didn't want their friends or family implicated in an way in what they were doing.

"That to me is just so sad that there are Canberrans who are clearly well loved and have a great network around them who could support them at a time when they chose to die. Federal legislation isn't protecting us from ourselves it's making it so much worse for people."

Ms Cheyne said she hoped people in Australian states got on board the campaign to allow the territory to legislate on the matter.

In a letter sent to Mr Morrison and federal Opposition Leader Anthony Albanese yesterday, Mr Barr said ACT and NT citizens deserved the same rights as anyone else.

"After 29 years of self-government the ACT has a robust and established parliament, a strong jurisdictional identity and an expectation that elected, local representatives will be able to debate and decide upon the issues that matter most to the ACT community," he said.

"The personal views of Senators and Members of Parliament on specific issues, such as marriage equality and assisted dying, should not be conflated with the legitimate argument to restore Territory rights."

"Denying this right fundamentally undermines democratic principles and prevents Territory citizens from deciding on the issues that matter most to their communities."

Earlier this month Western Australia became the second state in Australia after Victoria to legalise voluntary assisted dying.

The laws will be accessible to West Australian adults whose terminal illness causes intolerable suffering and is likely to cause their death within six months, or 12 months if the condition is a neurodegenerative one.