A body believed to be that of missing British backpacker Grace Millane has been found in bushland on the outskirts of Auckland on Sunday.

Detective Inspector Scott Beard said a formal investigation was yet to take place but the body, which was found in a bushland area about 10 metres from a Waitakere Ranges road, was believed to be that of the young tourist.

“Obviously, this brings the search for Grace to an end,” Inspector Beard told media. “It is an unbearable time for the Millane family and our hearts go out to them.”

A 26-year-old man, who was with Ms Millane when she was last seen at 9.41pm at an Auckland hotel on December 1, has been charged with her murder.

Police are searching for information about this rental car and where it was on Monday between 6am and 9.30am. Photo: Twitter/Tom Cheshire

Police also released images of a red Toyota Corolla hatchback, and asked anyone who saw the vehicle on the morning of Monday, December 3 between 6.30am and 9.30am to contact them.

The car was rented in central Auckland on Sunday.

New Zealand police had narrowed its search to a patch of bushland for the backpacker who went missing a week ago.

The tourist was last seen on CCTV footage arriving at the CityLife Auckland hotel with a man late on December 1 – the day before her 22nd birthday.

The 26-year-old man, who was tracked to an Auckland address, will be charged with murder and appear in court as early as Monday, police said.

Earlier on Sunday, Detective Inspector Beard said police were methodically combing an area of bush on Scenic Drive, a route along the city’s Waitakere Ranges regional park, about 20 kilometres west from the city centre.

“At this stage we are not able to confirm whether Grace has been located at this site,” he said.

Grace Millane was last seen by security cameras in central Auckland on the night she vanished. Photo: AP/NZ Police

A week-long search turned into a homicide probe, with officers saying while they had not yet found Ms Millane, a crime-scene examination of the hotel and video footage led to the conclusion she was no longer alive.

“Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide,” Detective Inspector Beard told reporters on Saturday.

Police say there’s no indication the unnamed man and his alleged victim knew each other before Ms Millane’s disappearance, but have not commented on how their paths crossed.

Ms Millane, from Essex, was on the second leg of a year-long trip around the world after graduating from university.

After visiting Peru, she arrived alone in New Zealand last month and had been in touch with family and friends almost daily until her disappearance.

Her father, David Millane, arrived in New Zealand on Friday, and made an emotional public appeal for help in finding Grace, who he described as a “lovely, outgoing, fun-loving, family-orientated daughter”.

-with AAP