Residents and tourists have fled wildfires in two more favorite Greek destinations, Corfu and Evia, even as the blazes that have gripped the island of Rhodes for seven days, prompting an evacuation that officials described as the largest in Greece’s history, spread onward into a village.

The new fires led the authorities to clear hundreds more people from hotels and homes in Corfu on Sunday night to safer areas on the island and to order evacuations on Evia on Monday. In Rhodes — where the British media has compared the relocation operation to the evacuation of troops from the French port of Dunkirk in World War II — tourists were still sleeping in schools, gymnasiums and hotel lobbies.

The outbreaks complicated the efforts of emergency services already battling blazes on Rhodes, where Greece’s military has been supporting the response. A military transport aircraft brought in hundreds of cots, sleeping bags and other provisions for displaced tourists and locals on Sunday evening. Another delivery was set to follow on Monday.

The village struck by fire on Rhodes on Monday was Asklipieio, in the island’s southeast.

On Evia, a fire spread in the south on Monday, prompting the authorities to order the evacuation of a village and another blaze broke out in the middle of the island.

The fight against the fires has drawn international support. The European Union has sent water-bombing aircraft and more than 450 firefighters to aid areas in Greece, the European commissioner for crisis management, Janez Lenarcic, wrote on Twitter on Sunday.

“Greece, we are by your side,” he wrote in Greek. Other countries including Egypt, Turkey and Israel have sent aircraft to help.

In Corfu, another popular tourist destination, more than 2,000 people were evacuated from 12 villages on Sunday night, Greece’s fire service spokesman, Vassilis Vathrakoyiannis, said at a news briefing. It was unclear how many of the evacuees were tourists.

Greece’s coast guard took part in the rescue, transferring many of the evacuees on Sunday night to safer parts of Corfu aboard patrol vessels and private boats. Television footage and videos posted on social media showed the night sky glowing orange as the fire advanced across a mountain ridge.

Greek television showed volunteers using tree branches on Sunday night to try to pound out a wildfire on a roadside on Corfu as firefighters used a hose to spray water into a larger blaze farther along the route. The fire on Corfu had been partially contained overnight, allowing some tourists to return to their hotels, according to state television.

As a fire in Rhodes continued to burn in the island’s southeast, airlines were able to ferry some travelers away from the island’s airport, where the authorities were distributing water and snacks to passengers. A total of 1,489 people left on overnight flights, mostly to Britain, Germany and Italy, Greece’s Civil Protection Ministry said.

The British Foreign Office also sent a team to Rhodes Airport to help with the relocation of British nationals.

Some airlines and the tour operators Tui U.K. and Jet2, which have suspended scheduled flights into the island, sent empty planes to Rhodes to bring travelers back.

While many tourists fled Rhodes, others said they wanted to stay and salvage what they could of their vacations.

Helen Tonks, from Cheshire in northern England, arrived on the island on Saturday night even as the fires raged and ended up being relocated on Monday to a hotel in the island’s northeast, away from the fires, after spending two days in a school with her husband and three daughters with military trucks bringing in provisions.

She felt like a hostage in the school, she said, while waiting for her tour operator to transfer the family from harm’s way, though she emphasized how helpful local people had been during their stay, regularly bringing them food and fresh fruit and offering them showers at their homes.

Efforts to douse the blazes came amid a blistering heat wave that has stoked tinder-dry conditions across Greece and much of southern Europe, which is recording some of the hottest temperatures of the year, representing a serious threat especially to older people and outdoor workers. In Greece, temperatures reached 45 Celsius, or 113 Fahrenheit, on Sunday and hovered at 44 Celsius in the south on Monday.

The combination of high temperatures and parched conditions made the firefighting response more challenging, Pavlos Marinakis, a Greek government spokesman, told reporters on Monday. Mr. Marinakis said Greece had had more than 50 new fires per day for 12 days in a row, or more than 600 in total.

“We are fighting a war, focused on the wildfires — we will rebuild what is lost,” Prime Minister Kyriakos Mitsotakis told Parliament on Monday ahead of a scheduled political debate.

Even as the heat dipped slightly on Monday, another heat wave — the third in three weeks in Greece — was forecast to grip the country from Wednesday.

“The risk of fire is extreme in many parts of Greece today, too,” Mr. Vathrakoyiannis, the fire service spokesman, said, urging people to “refrain from actions” that could spark new fires.

Greece’s fire service capabilities were stretched on Sunday as its members were called to a bridge that collapsed in the western city of Patra, killing one person and trapping several more.

Emma Bubola contributed reporting from London.