The wife of British TV presenter Michael Mosley said it is "devastating to have lost him" after her husband's body was found on the Greek island of Symi on Sunday morning, local time. 

Dr Mosley's body was discovered on day five of an extensive search on air, land and sea after he went missing on a walk during a holiday on Wednesday. 

"It's devastating to have lost Michael, my wonderful, funny, kind and brilliant husband," Clare Bailey Mosley said in a statement. 

"We had an incredibly lucky life together. We loved each other very much and were so happy together. I am incredibly proud of our children, their resilience and support over the past days."

Dr Bailey Mosley said her husband "Did an incredible climb, took the wrong route and collapsed where he couldn't easily be seen by the extensive search team."

"We’re taking comfort in the fact that he so very nearly made it," she said. 

She also thanked local authorities and residents of Symi who contributed to the search. 

"Some of these people on the island, who hadn’t even heard of Michael, worked from dawn till dusk unasked," she said. 

"We’re also very grateful to the press who have dealt with us with great respect."

"I feel so lucky to have our children and my amazing friends. 

"Most of all, I feel so lucky to have had this life with Michael."

Lefteris Papakalodoukas, the island's mayor, told The Associated Press he was on the boat with members of the media representatives when they saw a body some 20 meters above the Agia Marina beach on Sunday. 

“We zoomed with the cameras and saw it was him,” he said.

The mayor said that the body appeared to have fallen down a steep slope, stopping against a fence and lying face-up with a few rocks on top of it. 

"It is unclear if he had an accident or if he felt unwell," Mr Papakalodoukas told State TV ERT.

Police said he had been dead for several days. 

The body had a leather bag in one hand, said Antonis Mystiloglou, a cameraman with state TV ERT, who was also on the boat.

Another police official said the body had been found on rocky terrain, close to the sea, dismissing earlier reports that said he was found in a cave.

Police are investigating the scene.

The 67-year-old Mosley was holidaying with his wife on Symi when he went for a coastal walk on Wednesday afternoon, but did not return.

The deputy mayor said Mosley was found in a cave near the Agia Marina on the small island.

A broad search-and-rescue operation had been underway on the small island since Wednesday.

Mosley was last seen at 1:30pm on Wednesday, local time, when he went for a short stroll on his own from Agios Nikolaos beach to the fishing village of Pedi.

At first, authorities were concerned he went missing along the path, but on Friday CCTV images were released confirming Mosley had made it to Pedi about 20 minutes after leaving the beach.

Police say he took a coastal path, which is about 1.5 kilometres long and takes 20 minutes to walk. 

Mosley's wife, Clare Bailey Mosley, reported him missing on Thursday morning after he did not return.

Mosley's phone was found where he was staying with his wife, a police spokesperson told BBC News. 

Mosley is well known in Britain and Australia for popularising the intermittent fasting diet and rose to fame with appearances on the BBC.

In an earlier statement shared by Mosley's agent, Ms Mosley said the past three days had been "unbearable".

An extensive land, sea and air search continued on Saturday focusing on a different part of the island.

Searchers shifted their focus to between Pedi and the beach of Agia Marina.

The area is extremely rocky and mountainous. 

Symi is a small island, sitting on the eastern side of the Aegean Sea, about 6.5 kilometres from Türkiye's coast. 

The rocky island is 16km long and home to about 2,500 residents.

Mosley was a broadcaster well known in the UK for programmes including the BBC series Trust Me, I'm a Doctor. He also appeared on BBC's The One Show and ITV's This Morning.