HONG KONG — You might call it a Noah’s Ark for an era of melting polar ice sheets.

An audacious plan to respond to climate change by building a city of floating islands in the South Pacific is moving forward, with the government of French Polynesia agreeing to consider hosting the islands in a tropical lagoon.

The project is being put forward by a California nonprofit, the Seasteading Institute, which has raised about $2.5 million from more than 1,000 interested donors. Randolph Hencken, the group’s executive director, said work on the project could start in French Polynesia as early as next year, pending the results of some environmental and economic feasibility studies.

“We have a vision that we’re going to create an industry that provides floating islands to people who are threatened by rising sea levels,” Mr. Hencken said.

The group’s original founders included Peter Thiel, a billionaire investor and prominent supporter of President Trump, although Mr. Thiel is no longer donating to the institute, Mr. Hencken said.