The Northern Territory and ACT could soon have the power to legislate for voluntary euthanasia after a decision of the federal Labor caucus.

A private member’s bill to restore the rights of the territories to legislate on matters such as assisted dying will be introduced to federal parliament on August 1.

The Labor caucus on Monday agreed to allow a conscience vote on the bill, which will be introduced by NT-based MP Luke Gosling and the ACT’s Alicia Payne.

The caucus also agreed to allow debate on the bill during the time allocated for government business and in the Federation Chamber, which will speed up its progress through the lower house.

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 voluntary assisted dying 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 legislation allowing terminally ill adults to decide how to end their lives, the ACT and NT have been prevented from doing so.