The government is set to allow another hour of speeches on the territory rights bill on Wednesday morning, under an agreement which followed talks between Labor senator Katy Gallagher and independent David Pocock.

The allocation of extra time for the debate raises the chances that the private members' bill from Labor backbenchers Alicia Payne and Luke Gosling will be brought to a final vote before the end of the year.

Senator Pocock had planned to push for the upper house to sit late on Tuesday night to deal with the territory rights bill, amid fears the debate could drag on and threaten its prospects of success.

But he's instead agreed to support the government's wish to extend sitting hours on Tuesday so it can pass legislation to abolish the cashless debit card, which is its top priority for the rescheduled sitting week.

The former Wallabies captain has also agreed to delay his attempt to torpedo the government's plans to water down disclosure rules for superannuation funds.

READ MORE:

The government will allocate an hour on Wednesday morning for debate on overturning the so-called Andrews bill, which has blocked the territories from legislating on assisting dying since 1997.

The Canberra Times understands Senator Gallagher, who is the manager of government business, wants to keep finding windows of time to continue the debate in the hope of holding a final vote this year.

Senator Pocock believes the bill would pass if put to a vote right now.

But he fears the numbers could turn if anti-euthanasia groups are given more time to lobby senators.

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

We've made it a whole lot easier for you to have your say. Our new comment platform requires only one log-in to access articles and to join the discussion on The Canberra Times website. Find out how to register so you can enjoy civil, friendly and engaging discussions. See our moderation policy here.