Volunteers fought to extinguish a fire that blackened hills and charred buildings near Lindos, famous for its acropolis on a massive rock within its medieval walls.
“We have between 4,000 and 5,000 people now staying in different buildings,” Rhodes Deputy Mayor Thanassis Ferinis told Mega TV channel, calling for donations of necessities such as mattresses and bed linen.
Fire brigade spokesman Artobios said a pregnant woman and another person were taken to hospital due to the forest fires.
French, German, Dutch and British nationals were among the tourists in Rhodes, which one hotelier said could receive 150,000 visitors at peak time.
Artoboyos told Radio Sky that the evacuees, including villagers, were housed in hotels, indoor playgrounds, conference centers and school buildings, where they were provided with food, water and medical assistance.
A British tourist thanked the locals for their generosity, in an interview with Greek TV, saying that shops refused to pay for water and food and that small boats took the women and children to safety first, before returning to the men.
The Greek Ministry of Foreign Affairs said that it is in the process of establishing a help desk at Rhodes Airport to facilitate the departure of visitors who have lost their travel documents, in cooperation with embassies.
Video footage on social media showed crowds at the airport.
About 20,000 German tourists have been on the island, German tourism association DRV said, but only a small proportion were affected by the evacuations.
The company, Jet 2, which specializes in organizing tours, said that five planes that were scheduled to carry more tourists to the island will fly empty and will take people home on their scheduled flights. Air France-KLM said its daily flight from Rhodes was operating as normal. Ryanair said its flights to and from the island were not affected by the fire.
TUI said it had canceled all flights out to Rhodes until Tuesday. “Customers currently in Rhodes will return on their intended flight to their home country,” it added in a statement.
A French tourist in Lindos said he had seen an increased frequency of amphibious firefighting aircraft in the skies over the past few days. Television footage showed that the yellow planes were seen dredging into the sea.
“Everything is happening very quickly, we have seen more and more smoke,” the tourist, whose name was given only as Hugo, told French television.
Artobios said more than 250 firefighters were trying to contain the flames with the help of 18 aircraft. They battled on three fronts on Sunday, setting up fires to prevent the flames from spreading into dense forest or threatening more residential areas.
The fire has burned large areas of forest and many buildings since it broke out in a mountainous area on Tuesday.
Civil Protection warned of an extremely high risk of wildfires on Sunday in nearly half of Greece, where temperatures are expected to reach 45C.
Heatwaves can continue across southern Europe and many parts of the world until August.
Fires are common in Greece, but hotter, drier and windier summers have caused more of them to occur in recent years. An advisor to the World Meteorological Organization (WMO) said on Saturday that climate change means more frequent heat waves.