The upper house will sit for as long as it takes to reach a final vote on overturning a prohibition in place since the Andrews law passed in 1997.

Opponents are pushing for a last-minute amendment to Alicia Payne and Luke Gosling's restoring territory rights bill, which would place safeguards around future assisted dying regimes in the ACT and NT.

Politicians including ACT Chief Minister Andrew Barr and assisted dying advocates such as Andrew Denton are expected to fill the Senate's public gallery on Thursday night in anticipation of witnessing a historic moment for the territories.

Almost 9400 days have passed since the passage of Kevin Andrews' private members bill, which quashed the NT's world-first assisted dying laws and banned the territories from legislating them in the future.

The bill to overturn the ban appears all but certain to succeed after it last week passed the second reading stage 41 votes to 25.

Ten senators were absent from the vote, but even if all of them were opposed it wouldn't have been enough to turn the result.

That means only a last-minute change of heart from senators who voted in support at the second reading stage, which is considered extremely unlikely, can prevent the bill from passing.

Leading opponents including Liberal Jonathon Duniam last week conceded the bill would pass and have turned their attention to amending the legislation.

NT Country Liberal senator Jacinta Nampijinpa Price will move one amendment when debate resumes after 5.30pm.

Under the proposed change, the ACT and NT parliaments would be barred from passing future legislation which opened up access to assisted dying for under-18s.

The age restriction applies in each of the states' assisted dying regimes.

The amendment would also ensure that assisted dying could not be administered solely on the grounds of a person's disability or mental impairments.

The proposed change was circulated to senators and made public for the first time on Wednesday afternoon.

Senator Duniam will separately move a motion related to the approval process for drugs which can be used in assisted dying.

ACT senator David Pocock, who tried unsuccessfully to bring on a final vote during last week's debate, has dismissed the need for amendments, insisting the legislation before the senators was a "very simple bill".

MORE TERRITORY RIGHTS COVERAGE:

Alicia Payne and Luke Gosling's private members' bill doesn't make assisted dying legal in the territories - it simply lifts the ban on their parliaments debating and passing their own right-to-die laws.

"I said in the chamber that this is a very simple bill - it is simply repealing the Andrews bill," Senator Pocock said earlier this week.

"I understand this a tightly held issue and personal issue for many. But clearly there has been a lot of debate, not just this time ... but over the years."

In a speech in the Assembly on Wednesday, Mr Barr signaled the government would move quickly to progress assisted dying legislation in the ACT once the ban was lifted.

"This place will be particularly focused, I anticipate, on dealing with voluntary assisted dying legislation process that I imagine will take the entire calendar year," he said.

The Canberra Times has been calling for the repeal of the Andrews bill as part of its Our Right to Decide campaign.

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