The broadcaster's four children have now arrived on Symi to help in the hunt, according to the mayor of the Greek island.

Eleftherios Papakaloudoukas has said there is "no chance" the search, which has involved helicopters, drones and divers, will be called off until the 67-year-old is found.

But speaking through a translator, the mayor of 22 years questioned how anyone could survive in the heat that topped 40C (104F) on the day Mosley disappeared.

A search dog was only able to work for an hour on Saturday morning due to the temperature, as the search resumed, he added.

Mosley has not been seen since Wednesday when he set out for a walk on his own from Saint Nikolas Beach, where he had been with his wife Clare and another couple, to the centre of the island.

He was later caught on CCTV at 2pm in the fishing village of Pedi, around 1.2km away.

Footage from a restaurant showed Mosley wearing a dark T-shirt, shorts and a cap, carrying an umbrella.

A separate video taken from a house at the edge of Pedi appears to show him entering a mountainous path heading inland.

His wife, who is also a doctor, raised the alarm after he failed to return.

Mosley did not have his mobile phone with him, hampering tracing efforts.

One of the rescuers said: "The path is not easy to follow, if he took a wrong turn, he would be lost.

"He could be anywhere, it is a race against time."

The search for Mosley resumed at 6am on Saturday, with teams scouring a 6.5km radius over a mountainous area, which search organisers described as "very dangerous".

Read more about missing TV doctor:
What we know about his last known movements
Son reveals surreal parallels with case of missing dad

Mr Papakaloudoukas said the area the missing Briton is believed to have ventured into is "only rocks" and "difficult to pass", with "loads" of snakes.

He added: "He chose paths which are very difficult to walk in such temperatures and under any circumstances."

Mr Papakaloudoukas hoped Mosley was found "safe and alive" and said "all the community is so sad about this". He added it has "never happened before".

The mayor's daughter Mika said "a lot of" island residents had joined the search using their own boats to find the British national.

She added: "It's such a small island to get lost on. It's so weird for us. Everybody is worried and looking for him."

Authorities have considered a number of possibilities for Mosley's disappearance, including that he may have suffered a fall or been bitten by a snake, according to reports.

Mosley, his wife and the other couple are understood to arrived in Symi for a week's holiday on Tuesday.

Mosley is a columnist and presenter who has made a number of films about healthy living.

Known for popularising the 5:2 diet, he fronted the Channel 4 show Michael Mosley: Who Made Britain Fat? and was part of the BBC series Trust Me, I'm A Doctor.

He has also appeared on numerous daytime television shows and hosts the health podcast, Just One Thing.