“They went out for a walk yesterday in the heat,” he said, “and now we can’t find them.”

Mr. Marakis, who was participating in the search, told Greek television on Saturday that a search for the two women had started on Friday, noting that one had her cellphone off and the other did not have it with her.

One of the women sent a text message to the owner of the room where she was staying at 8:24 a.m. Friday, saying, “I’ve fallen. I don’t feel well,” Mr. Marakis said.

The body of Mr. Mosley, 67, the British medical journalist, was found on June 9 on rocks next to a beach in Agia Marina, on the island of Symi, after a five-day search. He had been reported missing by his wife, Clare Bailey, a day after the couple arrived for a weeklong stay, according to the police spokeswoman. He had gone for a walk across what local officials described as “rugged terrain” as temperatures on the island had been hovering around 95 degrees Fahrenheit.

On Friday, an 80-year-old Belgian man who had been walking with a group died near the ancient site of Lato in eastern Crete, according to the police spokeswoman. Two other tourists — a 70-year-old Frenchwoman and a Dutch man, also 70 — also died early this month during treks in different parts of Crete, Ms. Dimoglidou said.

As the latest hot spell peaked on Wednesday and Thursday, the authorities closed many schools in Athens, and visiting hours were restricted at several ancient sites, including the Acropolis, Greece’s most popular.

The Acropolis resumed regular visiting hours on Friday as temperatures dipped slightly, but restrictions remained in place for the ancient site of Knossos on Crete, where temperatures were forecast to reach 40 degrees Celsius, or 104 Fahrenheit. Sites on Crete would close from 1 to 5 p.m. if temperatures exceeded 40 Celsius, Greece’s Culture Ministry said.