Labor backbenchers Alicia Payne and Luke Gosling will attempt to gain parliamentary support for their bill, which would allow territory governments to legislate on voluntary assisted dying.
The NT government passed a world-first law to legalise euthanasia in 1995.
But the so-called Andrews Bill - named after former Liberal MP Kevin Andrews who introduced it in opposition to the legislation - passed federal parliament in 1997, invoking a constitutional power which enables federal parliament to overturn territory laws.
While every state government has since passed laws to allow terminally ill adults to decide how to end their lives, the ACT and NT have been prevented from doing so.
Leaders at the University of Canberra (UC) and Charles Darwin University (CDU) say passing the bill would restore the right of self-determination to the citizens of the ACT and NT.
The proposal from the territory MPs will address a "long-standing blight" on Australian democracy, UC vice-chancellor Paddy Nixon said.
"It is not our usual practice to speak out on legislation before the parliament, but this legislation is critical," he said.
"UC and CDU are the only universities in Australia established under territory legislation and so the rights of Territorians are of critical importance to us."
Prime Minister Anthony Albanese will allow Labor MPs a conscience vote on the matter when it is presented to parliament.
Northern Territory MP Luke Gosling is confident his bid to restore territory rights will have the support necessary to pass both houses.
"All we are doing is saying we're sick of being treated as second-class citizens, and I use those words when I talk to our (parliamentary) colleagues," he told Darwin radio 104.9M on Wednesday.
"I am confident that territorians will receive the support of the parliament and we'll all right that wrong."
But Catholic Archbishop of Canberra and Goulburn Christopher Prowse has written to federal parliamentarians, urging them to "deeply reflect" on the proposition.
He argues the proposal does not aim to restore all territory rights, but is rather solely aimed at allowing legislation "for state-sanctioned killing through euthanasia".
"My view is that a radical change to society's most foundational law - overturning the prohibition on the intentional killing of citizens - is ethically unjustifiable, cannot ensure legal protection of the vulnerable and would fail to uphold the dignity of the dying," he wrote in the letter.
The ACT is prevented from establishing its own police force or developing censorship legislation, but these issues are not presented as limiting democracy, he said.
"Legislation directly and specifically aimed at enabling lethal injections is difficult to reconcile with (parliament's) responsibilities to the common good or the dignity of the person," he said.
But Mr Gosling said the proposal will ensure the "conscience decision" is made by the territories, not the Commonwealth.
"It's a matter of record that I want to see palliative care strengthened and I'll keep advocating for that," he said.
"I'll work with NT colleagues to make sure that if there is legislation in the future on voluntary assisted dying that there's appropriate safeguards in there to ensure that vulnerable people are protected."
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