Northern Territory police has announced a $500,000 reward in a bid to locate the remains of a British backpacker who was murdered in the Northern Territory in 2001.

Peter Falconio, 28, and his girlfriend Joanne Lees were driving about 300km from Alice Springs, when they were flagged down by Bradley John Murdoch, who said they had mechanical issues.

Falconio went behind the car with Murdoch to investigate the issue, when Lees heard a gunshot. Falconio was never seen again.

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Acting Commander Grieve said police want to bring “resolution” to Falconio’s family.

“(Police) recognise that there are certain times when there is the potential for opportunities to be taken advantage of,” he said.

“We believe now is the right time, to come forward with a reward.

“There was a previous reward of up to $250,000, so we’ve upped that to up $500,000.

“It’s like any ongoing police investigation. You want to solve it.”

Murdoch, who has never divulged the whereabouts of Falconio’s body, has remained silent.

Currently serving a life sentence, Murdoch was this week transferred from jail into palliative care in Alice Springs Hospital.

Murdoch cable-tied Lees and covered her head but she managed to escape and hid in bushland for five hours while Murdoch searched for her with his dog before she managed to flag down a truck driver.

He has maintained his innocence and pleaded not guilty, but was convicted of murder in 2005.

Several extensive police searches have failed to locate his remains.

“You want to try and at least bring some sliver of resolution to Peter’s family, by bringing home his remains,” Grieve said.

The officer who arrested Murdoch two decades ago doubts he will have a change of heart.

“I think for Bradley Murdoch, he’s maintained his innocence,” Colleen Gwynne said.

“He’s never said to anyone that he’s guilty of this.

“I think for him it’s a part of his control that he will never disclose. He will take it with him. It’s unfortunate for the family that’s what he’s chosen to do.”