Senator McMahon says the door remains open for the ACT to be included if the bill progressed to debate, declaring it was Labor senator Katy Gallagher's "one big chance" to back up her rhetoric with action to help the territory she once led regain the right to legislate on the issue.

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The Country Liberal senator on Wednesday afternoon introduced a bill to restore the NT's powers to make its own euthanasia laws, which it was stripped of by the so-called Andrews Bill more than 24 years ago. That bill also blocked the ACT from legislating on voluntary assisted dying.

"My bill is basically to right a wrong that was done 24 years ago [when NT laws were overturned]," Senator McMahon told The Canberra Times.

"The people of the NT felt extremely aggrieved when their legislation was overturned, and have been so ever since.

"They've felt harshly done by and upset that the Commonwealth had come over the top and taken away a piece of legislation that was quite valued. They have been quite keen to get the right to make the legislation ever since then."

The private member's bill also removes limitations on the NT Parliament related to land acquisitions and workplace laws.

Senator McMahon decided to exclude the ACT from her bill after her Morrison government colleague and ACT senator Zed Seselja signalled he wouldn't support it.

After the ACT's omission was reported in the media, Canberrans began contacting the NT senator urging her to include both territories.

Speaking to The Canberra Times before the bill was introduced, Senator McMahon said she "felt sorry for the people of the ACT".

"There has definitely been a significant number of phone calls and emails [from Canberrans], but their senator [Zed Seselja] does not support it," she said.

Of all the attempts to repeal the Andrews Bill in the past three decades, this is the first time the push has been led by a member of the government. Senator McMahon is set to leave Federal Parliament at the next election after losing a preselection contest.

Senator McMahon again invited Senator Gallagher, a former ACT chief minister, to amend her bill to include the ACT if and when it reached debate.

"Quite honestly, if Katy supported it [territory rights] why, honestly, is she saying that she wouldn't move an amendment? This is her one big chance," she said.

The Labor frontbencher has firmly rejected Senator McMahon's prior invitations, insisting that a straight repeal of the so-called Andrews Bill was the "only way" to restore the two territories' right to legislate on voluntary euthanasia.

Senator McMahon said her bill was about territory rights, not voluntary assisted dying - which she personally supports, provided safeguards are in place.

"For me it is to right the wrong," she said.

"Yes, I realise that people are going to say it's a euthanasia bill - it is not."

Debate on the bill was adjourned on Wednesday afternoon.

Senator McMahon said she was "quite optimistic" that the bill would have the numbers to pass both houses of parliament if it was brought on for debate.

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