Missing toddler Ben Needham is believed to have died as a result of an accident, police have said.
Detectives from the South Yorkshire force formally ended a three-week search of Kos on Sunday afternoon, and at a press conference on the Greek island revealed they had discovered an item thought to have been with the youngster at the time of his disappearance on July 24 1991.
The search operation was prompted by information that a digger driver may have been responsible for the Sheffield boy's death, as he was clearing land with an excavator near where Ben was playing on the day he vanished.
Speaking at the scene, Detective Inspector Jon Cousins said: "My team and I know that machinery, including a large digger, was used to clear an area of land on 24 July 1991, behind the farmhouse that was being renovated by the Needhams. It is my professional belief that Ben Needham died as a result of an accident near to the farmhouse in Iraklis where he was last seen playing.
"The events leading up to and following that incident have been explored by my team of experts to great lengths. The fact that we have not had a direct result during this visit to Kos does not preclude the facts that we know to be true.
"An item found on Saturday, which I have shown personally to some of Ben's family, was found in one of the targeted areas at the second site, very close to a dated item from 1991.
"It is our initial understanding that this item was in Ben's possession around the time he went missing."
Mr Cousins said the recovery of the item added to his belief that material had been removed from the farmhouse on or shortly after the 21-month-old disappeared.
Despite this stage of the investigation coming to an end, the officer pledged to continue searching for answers, and paid tribute to Ben's family.
He concluded: "We remain committed to the investigation and it will not simply close; myself and Detective Superintendent Matt Fenwick will retain ownership of it and if new information comes to light, we will investigate it thoroughly.
"We will not stop in our quest to find further answers for Ben's family."
Speaking before the briefing, the toddler's mother, Kerry Needham, told the Daily Mirror she wanted to "tear up" the whole Greek island.
She said: "They know he's dead but just can't find him. Police said it's time we ended our 25-year search. They are right but I can't say goodbye knowing he's still on that island somewhere. I feel physically sick. I can't feel any worse than I do.
"He didn't leave Kos, he didn't walk away ... Somebody didn't take him, so he's here somewhere. They believe he is there but they can't dig in everyone's gardens or homes that have been built over the years. I want to tear up the whole island to find him.
"Someone knows where he is. For God's sake, help me find him. We know he's dead but we need to find him. When someone dies you find a special place."
The digger driver, Konstantinos Barkas, also known as Dino, is believed to have died from stomach cancer last year.