Instead, delegates voted to "encourage" all federal Labor parliamentarians to support reinstating voting rights for the territories when the matter comes before the federal parliament.

The original motion, moved by ACT Chief Minister Andrew Barr and seconded by Northern Territory Deputy Chief Minister Nicole Mansion, called on the conference to support a binding vote on all federal Labor politicians to support repealing the Andrews Bill, which was introduced to bring an end to the Northern Territory's assisted dying scheme in 1997.

It read: "Labor believes this democratic right should be held by all Australians irrespective of the state or territory in which they reside. This conference believes it is unacceptable that as a result of the Andrews Bill Australians who reside in the ACT and NT have less democratic rights than other Australians."

The binding vote would not have extended to the actual issue of euthanasia, which is a conscience matter for Labor.

However the motion was amended to remove the binding vote and was unanimously passed.

Mr Barr said the ACT government would continue to campaign for the repeal of the Andrews Bill next year.

"It is simply not fair that some Australians should have fewer democratic rights than others based on where they live," Mr Barr said.

"The National Conference’s clear and positive endorsement of territory rights makes it more likely that repeal can succeed next time."

Labor senator Alex Gallacher was one of several senators who changed their mind at the last minute and voted down a bid to revoke the Andrews Bill championed by Liberal Democrats senator David Leyonhjelm in August. The bill fell just two votes short.

ACT-based Labor MP Andrew Leigh also introduced a private member's bill to repeal the legislation around the same time, which remains on the notice paper.

Since the Leyonhjelm bill was rejected, Queensland has launched an inquiry into legalising euthanasia.

Western Australia has also indicated it will legalise euthanasia in the second half of next year.

However the campaign to restore territory rights will likely kick back into gear after next year's federal election. The renewed push will depend heavily on the make-up of the Senate.

Mr Barr's motion to restore funding to Australia's national cultural institutions was also passed on Monday.

It asked for federal Labor to commit to sustainable funding, deliver long-awaited expansions and invest in the cultural inclusion of Aboriginal and Torres Strait Islanders in all national cultural institutions.