“We will not lose hope,” the wife of missing TV and radio presenter Michael Mosley has said, as the search continues on the Greek island of Symi.

The 67-year-old vanished after setting off on a walk on Wednesday.

His wife Dr Clare Bailey Mosley said in a statement that the days since he went missing had been “the longest and most unbearable”.

On Saturday, a search and rescue operation resumed for Dr Mosley, known for his TV programmes and BBC Radio 4’s Just One Thing podcast.

In her statement, Dr Bailey Mosley said: “It has been three days since Michael left the beach to go for a walk. The longest and most unbearable days for myself and my children.

“The search is ongoing and our family are so incredibly grateful to the people of Symi, the Greek authorities and the British Consulate who are working tirelessly to help find Michael.

“We will not lose hope.”

Dr Bailey Mosley has been searching the island assisted by friends. The couple’s four children have also arrived on Symi to help with the search.

Michael Mosley went missing on Wednesday after leaving his wife on Agios Nikolaos beach around 13:30 local time (11:30 BST).

His wife later reported Dr Mosley, who did not have his phone, missing.

BBC News has seen new CCTV – one of the last-known sightings – of a man believed to be Dr Mosley walking with an umbrella next to the marina in the village of Pedi on Wednesday, heading towards rocky hills.

The new footage appears to show the man in good form and walking steadily, an unnamed police officer told BBC News.

Greek authorities have since shifted their search operation to this part of the island.

In the mountainous terrain it would be easy to fall and injure yourself, or wander off the trail and get lost.

One theory that has emerged is that Dr Mosley was trying to take a much longer route than previously thought, passing over miles of exposed hillside. Dr Mosley’s accommodation was in the main town about 1 mile from Pedi.

When BBC News walked a short bit of the same path Dr Mosley is believed to have followed, under the midday sun, the effects of the heat could be felt quickly.

So far, police and firefighters have been using drones, a helicopter and a sniffer dog to try to locate the missing presenter.

Divers have also been looking in the water, as well as patrol boats, private boats and commercial boats, Symi’s coastguard said.

Symi’s mayor Eleftherios Papakaloudoukas said the search will continue until Dr Mosley is found.

He added he was unsure why the missing presenter would try to make a long, potentially arduous journey in such heat, but he hoped the presenter is found “safe and alive”.

Before moving into TV, Dr Mosley studied medicine in London and qualified as a doctor but for the last couple of decades has been working as a presenter, documentary maker, journalist and author.

He has appeared on BBC One’s The One Show and ITV’s This Morning.

Dr Mosley is also columnist for the Daily Mail and his TV programmes also include Channel 4 show Michael Mosley: Who Made Britain Fat? and BBC show Trust Me, I’m A Doctor.

His wife Dr Bailey Mosley is also a doctor, author and healthy living advocate.

The couple recently appeared at the Hay Festival where Dr Mosley presented a special edition of Just One Thing.

Reacting to the “shocking news”, his fellow Trust Me, I’m A Doctor co-star Dr Saleyha Ahsan said she was “praying he is found safe” and she feels “sick with worry”.

On Thursday’s edition of The One Show, presenter Alex Jones opened the programme by expressing concern that “our friend” had gone missing.

“Our thoughts are very much with his wife Clare and the rest of his family at this worrying time. We hope for more positive news,” she added.

Wednesday 1330 local time (11:30 BST) – Dr Michael Mosley leaves his wife Clare on Agios Nikolaos beach and sets off on a walk

1350 – Man carrying umbrella is seen on CCTV in Pedi

1357 – Same man is seen again at Pedi’s marina heading north-east

Thursday 1115 – Police are unable to find the presenter, so they inform Athens and request assistance from the Greek fire department

1400 – Greek fire services, with six firefighters and a drone team, arrive in Symi

1900 – Helicopter deployed to assist search

Friday – Divers join the search in the water around Symi

Saturday 0600 – Firefighters resume search for Dr Mosley

1400 – His wife Clare says the Mosley family “will not lose hope” and thanks those involved in the search

Additional reporting by Insaf Abbas in Symi and Andre Rhoden-Paul in London