To house the evacuees of Grindavik, the Icelandic town where lava poured into some houses last week after a volcanic eruption, a former prime minister proposed building a new town from scratch. A politician said Airbnbs around the island nation should be restricted to make room for the residents. And a radio host suggested turning away asylum seekers to focus resources on helping “refugees” from Grindavik.

“To evacuate 1 percent of the nation,” Prime Minister Katrin Jakobsdottir said, “is a major challenge.”

Grindavik, a fishing town in southwestern Iceland, is still under the threat of volcanic eruptions, and experts consider it uninhabitable in the near future. About 3,700 people lived there before the eruption, a significant number of residents for Iceland, whose total population is only 400,000. The authorities are scrambling to house the residents and contain their financial losses, and the issue is dominating the national debate.

Residents of the town are living in hotel rooms, in summer cottages, in temporary rental apartments or are being hosted by family members.

Thorgerdur Eliasdottir, 67, a restaurant worker from Grindavik, said that she and her cat had moved five times since the town was first evacuated in November. She said that she planned to move again soon, to an apartment that she will be able to rent for three months.

“I have an old timber house in Grindavik,” she said in a telephone interview. “I wish the government would simply put it on a car and drive it to a safe location.”

The Icelandic housing market was already saturated with a combination of population growth and tourism, which has picked up again after the pandemic. More than 8,000 bedrooms in the capital region were available for short-term rental as of last summer, according to Iceland’s tourist board.

For those interested in buying a home, interest rates are at more than 9 percent.

Fannar Jonasson, the mayor of Grindavik, whose office has moved to City Hall in the capital, Reykjavik, said the scarcity of places to live meant residents were now scattered around the country, with many struggling to find long-term housing.

“On all fronts, we are now working toward a long-term solution,” he said Thursday in a phone interview.

Grindavik’s population has grown rapidly in recent years because of an influx of people from Reykjavik, which is only about 30 miles away.

After the eruption, banks agreed to freeze mortgage payments for the residents, but residents said they could not get insurance payouts unless their houses were directly destroyed.

Bryndis Gunnlaugsdottir, a lawyer and a former resident of Grindavik, said that when she saw her neighbor’s house under the lava, but saw her own house still standing, “it was the worst moment since the evacuation.”

Speaking Tuesday at a packed town-hall-style meeting with politicians and scientists, she added that if her house had gone up in flames, her financial stress would ease.

“The noose around my neck would disappear,” she said, because her home would have been covered by insurance.

The government is now partly subsidizing the rent of Grindavik’s former residents, but lawmakers are discussing a bill that would allow the government to buy all the homes there and then offer them back to the former owners once the area was considered safe again.

Vilhjalmur Arnason, a lawmaker and resident of Grindavik, said that that would be the only way to answer the locals’ demands.

“Let us build a new home now,” he said in a phone interview as he left a meeting with the government’s finance committee in Reykjavik. “So we can find a new point to start on.”

Volcanologists said that, according to predictions, the volcanic activity on the southwestern Reykjanes Peninsula, where Grindavik is, was going to last 10 to 20 years. Recent earthquakes have also created cracks in the town, and last month, a construction worker fell down a crater believed to be 40 meters, or more than 130 feet, deep. He is presumed dead. The eruption also broke the main pipeline channeling hot water into Grindavik’s homes.

“The grounds for people to inhabit Grindavik are not in sight,” said Magnus Tumi Gudmundsson, who advises the civil defense agency.

But Mr. Gudmundsson added that the volcanic activity could move away from the craters menacing Grindavik, allowing the town to be safe again.

Gisli Palsson, an anthropology professor who studied the impact of a 1973 eruption on the Westman Islands, the last time a volcanic eruption displaced part of Iceland’s population, said that the doomsday predictions for Grindavik reminded him of the despairing tone in the first weeks after the eruption there.

“At first, many people said it was over for the town,” he said. But, he added, when the eruption stopped, many people, who had strong roots in the area, eventually went back.

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