It is no secret that many Americans are worried about inflation and the high cost of groceries, and those concerns were a driving factor in Donald J. Trump’s victory.

Now a Democratic candidate for mayor of New York City is seizing on that anxiety and proposing that the city open its own grocery stores to bring down costs.

The idea has gained momentum in other cities as a way to address so-called food deserts, where supermarkets are scarce. Chicago and Atlanta are moving forward with proposals, and there are already city-owned grocery stores in Kansas and Wisconsin.

Zohran Mamdani, a democratic socialist state lawmaker who is running for mayor of New York City, will announce a plan on Thursday to build five municipal grocery stores — one in each borough.

“Everywhere I go, I hear New Yorkers talking about the outrageous prices of groceries,” he said in an interview. “This is a bold and workable plan.”

Mr. Mamdani released a video last month, which went viral, featuring voters in working-class neighborhoods who supported Mr. Trump. Many expressed concerns about the cost of living, reflecting a feeling that is evident across the nation.