A 73-year-old French woman missing on the Greek island of Sikinos sent a distress message to her hotel saying she had suffered a fall before her disappearance.

A search is under way for the woman, who has not been named by authorities. She is one of three tourists missing in Greece, and five have died this month in unseasonably hot weather.

Ilias Gavanas, who owns the guest house where the woman was staying, told Reuters he last heard from her on Friday when he reached her by phone at around 8.30am after missing a call from her at 5.50am.

He said the woman had sent him a selfie and a message saying: “I am fall.” He replied in French and English asking for her location and telling her to call the European emergency number 112, and alerted police and municipal authorities.

Temperatures soared above 40C across Greece earlier this month.

‘Don’t go out in the heat’

Hiking is popular with tourists on Sikinos, a largely barren and sparsely populated island in the southern Aegean Sea, Mr Gavanas said.

“We warn them not to go out in the heat, to always inform us where they are, to not wander off alone,” he said. “It was 40 degrees.”

The tourism ministry said it “remained vigilant” and was working with other ministries to ensure travellers were being kept informed.

A second French woman is missing on Sikinos, and authorities believe the two missing women went hiking together although they were not staying at the same hotel, police said.

A search is also under way on the island of Amorgos for an American man missing since June 11.

The five tourists who have died included Michael Mosley, the doctor and television presenter whose body was found on the island of Symi. A 55-year-old American died on the Ionian island of Mathraki, a 74-year-old Dutch tourist died on the island of Samos and two hikers died on Crete.