Senators are being urged to scrap "undemocratic" laws blocking Australian territories from legalising voluntary euthanasia.
Legislation passed by the federal parliament two decades ago banned the ACT and North Territory controlling their own laws on euthanasia.
The chief ministers of the territories have taken out a full-page advertisement in The Australian calling on the Senate to restore the right for their residents to decide what laws apply to them.
"Voting for this bill doesn't mean there will be assisted dying in the NT or the ACT," Andrew Barr and Michael Gunner wrote in an open letter titled "It's about our rights'."
"It will simply give territorians the same right to decide on it as other Australians."
Meanwhile, pressure is mounting on the prime minister to keep a deal with a federal senator to vote on voluntary euthanasia in both houses ahead of parliament.
Senator David Leyonhelm says he was guaranteed a vote in both houses in return for his support for re-establishing the Australian Building and Construction Commission.
The Liberal Democrats senator said staff witnessed the deal struck with Mr Turnbull, which the prime minister has since denied was agreed on.
"He has a problem with his own party. There are conservatives within his party who basically, they hate the prime minister more than they hate the opposition for reasons best known to themselves," Senator Leyonhjelm told ABC TV on Sunday evening.
"They are looking for every opportunity to give him a hard time. He is very sensitive to that. They are social conservatives so he did not want to give them any ammunition."
Senator Leyonhjelm said he wouldn't give his support for upcoming legislation, including on industrial relations and a tax on NBN customers,- coming up in the Senate until the deal is kept.
"I am not feeling vindictive about this, I am just annoyed that what was a deal appears no longer to be a deal in the eyes of the government," he said.
"Until they are prepared to accept that's the deal and they stick to the deal ... there are 50 or 60 bills waiting in the queue to be dealt with. For me to go either way is pretty easy."
The coalition needs eight-of-the-10 independent, One Nation and Centre Alliance senators to pass its legislation.
The upper house is expected to debate Senator Leyonhjelm's legislation on Tuesday.