The private members bill from Liberal Democrats Senator David Leyonhjelm suffered a shock defeat in the Senate overnight, after several senators reversed their support, including Liberal Anne Ruston, Nationals Steve Martin, Labor's Alex Gallacher, and crossbenchers Brian Burston and Peter Georgiou.

The bill was widely tipped to pass the Senate by a slim margin, however the tide began to turn on the second day of debate, amid intense lobbying from groups opposed to voluntary assisted dying.

In the end it was defeated by two votes. 

Chief Minister Andrew Barr vowed this would not be the end of the push for territory rights.

"Canberrans have been let down by the Australian parliament, again, after the Senate narrowly rejected reforms that would have allowed the ACT and the NT to consider our own voluntary assisted dying legislation," Mr Barr said.

"I want to thank the 34 Senators who stood up for the Australian territories and the communities we represent. It is disappointing that we fell two votes short tonight, but we will not give up. The restoration of territory rights will be back before the parliament soon."

He said marriage equality advocates had experienced similar setbacks before same-sex marriage was legalised.

“I recall many people telling me there was no way that marriage laws would ever change and we kept chipping away at that and worked across the nation to garner sufficient support for that to happen. I think a similar approach can work here," Mr Barr said.

The chief minister also moved an unusual remonstrance motion to formally express the territory's displeasure with the Senate over the failed vote.

It was the first remonstrance motion to pass in the ACT parliament's history.

Another remonstrance motion was moved in 2009 after the federal government interfered with the Civil Partnerships Amendment, however it was watered down and passed as just a regular motion.

The ACT Legislative Assembly also endorsed a remonstrance motion passed by the Northern Territory's parliament in 1996 after their euthanasia laws were quashed by the Commonwealth.

The list of grievances will be presented to the president of the Senate, and accuses senators misrepresenting the intentions of the ACT parliament and conflating their own personal views on euthanasia with the issue of territory rights

It also criticised senators for drawing on debunked sources and for reneging on previously stated positions at the last minute.

The Liberals treated the motion as a conscience issue so Nicole Lawder, Jeremy Hanson, Mark Parton, and Elizabeth Lee were able to put on the record for the first time their desire to restore territory rights, despite their concerns about euthanasia.

ACT Opposition leader Alistair Coe denied that his party members had been restricted from speaking out before the vote, rather that they wanted democracy to run its course.

“Members have always been able to do what they wish on this issue, the Canberra Liberals have never had a strong arm approach on this policy issue or any other," Mr Coe said.

Mr Barr said advocates for territory rights would continue to target politicians on the hill over the next year in the hope that a change of government may shift a few votes their way.

He added territory rights would likely be a federal and territory election issue.

"People have a pretty clear choice between the two leaders of the major parties as to who is going to advocate strongly for territory rights and who isn’t," Mr Barr said.

Greens crossbencher Caroline Le Couteur remained optimistic the territories rights to legalise euthanasia would one day be restored.

Ms Le Couteur was scathing of ACT Senator Zed Seselja, who voted against restoring territory rights because he was concerned about the kind of scheme the Labor-Greens government would introduce. She said Senator Seselja should reflect on his role in this debate.

"Given the small margin, the Senator refused to allow our community to decide for ourselves - instead, he felt his own views more important than those of the Canberra community. He also could have urged his colleagues to simply allow Canberrans to have their own say," Ms Le Couteur said.

“The people of the ACT are tired of being treated as second class citizens. While bowed, we remain undeterred. The fight to restore territory rights will continue.”

The lower house could be forced to confront the issue next week when a private members bill similar to the one voted down by the Senate appears on the notice paper.

That bill is co-sponsored by Canberra MP Andrew Leigh and his Labor colleague, Northern Territory MP Luke Gosling.

However if Prime Minister Malcolm Turnbull doesn't grant leave for debate, the majority of the house would have to vote to suspend standing orders for debate to occur.

Given Labor does not hold the numbers in the lower house, even with their whole party and the entire crossbench on board, it is unclear if or when the issue of territory rights will be debated again.

However Mr Leigh said he would keep up the pressure.

"It's always tough for the opposition to get a private members bill debated in the house, the government controls the agenda," Mr Leigh said.

"[The Senate vote] wasn't resounding, only two people switched sides. Moving motions in both places is important to keep the conversations going. We can push hard to make sure the voices of territorians are heard."