Greens Leader Bob Brown says he will again try to overturn a ban that prevents the Northern Territory and the Australian Capital Territory passing laws allowing euthanasia.

In 1995 the Northern Territory Government passed voluntarily euthanasia laws, but the Federal Government overturned them two years later.

Senator Brown has previously been unsuccessful in his bid to have the ban lifted.

He has told Channel Ten restoring the issue is once again at the top of his agenda.

"What is unarguable here is that the territories should have their rights to legislate on euthanasia restored," he said.

"It will effectively be a debate about the people of the territories to have their elected assemblies legislate for euthanasia."

The Opposition's Christopher Pyne has hit out at the Greens, saying he expected them to focus on issues like euthanasia, instead of on the economy.

"The Greens will ensure that in their alliance with the Labor Party we are pursuing rabbits down every hole," he said.

"I'll be very concerned if the 43rd Parliament means that Australia is worse off in three years."

Meanwhile, five pro-euthanasia groups have united to support another move to legalise the practice in South Australia.

Greens MP Mark Parnell and Labor backbencher Steph Key last week introduced identical bills in both houses of the South Australian Parliament.

John Willoughby of the South Australian Doctors Supporting Choice for Voluntary Euthanasia says his experiences as a doctor - and seeing people in immense pain and suffering - prompted his action on the issue.

"It is unacceptable that people should be forced to endure situations that they do not wish to endure for themselves," he said.

"Sooner or later, everyone is going to recognise that, including our politicians."

The ACT Government says it would not necessarily support euthanasia legislation but says it should have right to do so.

ACT Attorney-General Simon Corbell says residents are not being treated equally.

"The issue of euthanasia is the one issue where the territories are specifically barred from even considering in the Parliament and that is fundamentally undemocratic," he said.