Bradley John Murdoch was given a life sentence for murdering the 28-year-old and assaulting and attempting to kidnap his girlfriend Joanne Lees on the Stuart Highway in the Northern Territory in July 2001.
Ms Lees hid in bushland for five hours while Murdoch hunted her with his dog before she managed to flag down a truck driver.
The case involving two British backpackers touring Australia in a camper van prompted global media attention.
In 2005, Murdoch was convicted of the execution-style shooting murder of Mr Falconio and was given a life sentence with a non-parole period of 28 years.
He is believed to have hidden Mr Falconio's body, which has never been found despite extensive searches.
The announcement of a reward of up to $500,000 - double the previous incentive in place - comes as the terminally ill Murdoch is reported to be on his deathbed in hospital in Alice Springs.Â
Northern Territory Police acting commander Mark Grieve said officers still hoped someone had information that could lead to the body's discovery.
"We recognise the passage of time that's transpired, however it's never too late to reach out and start that conversation with police," he said on Wednesday.
"There may be someone out there he's confided in. Whether or not that's family or friends, we just don't know."
Mr Falconio and Ms Lees were on the Stuart Highway north of Alice Springs on July 14, 2001, when Murdoch drove up behind them, the murder trial heard.
He indicated for them to pull over, saying their van might have an engine problem.
Mr Falconio went behind the car with Murdoch to investigate before Ms Lees heard a gunshot.
Murdoch then cable-tied her and covered her head, but she escaped and hid in bushland while the killer tried to hunt her down.
Mr Grieve said police had over the years made numerous approaches to Murdoch for information on where Mr Falconio's remains lay, including within the last week.
"On all occasions he's chosen not to positively engage with police," he said.
Police wanted to solve the case in full, Mr Grieve added.
"You want to try and at least bring some sliver of resolution to Peter's family, by bringing home his remains," he said.
The UK-based Falconio family had been informed of the reward offer, Mr Grieve said.
A $250,000 reward for information that could help convict Mr Falconio's killer was previously put in place and several applications were made to share in the funds after Murdoch's conviction.
In 2019, the killer was diagnosed with terminal throat cancer.
Mr Grieve declined to comment on reports Murdoch had recently been allowed out on excursions while in palliative care.
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