WASHINGTON—President Biden called on the Federal Trade Commission to investigate whether oil-and-gas companies are participating in illegal conduct aimed at keeping gasoline prices high, in the latest effort by the White House to respond to public concerns about costs for everything from fuel to groceries.

In a Wednesday letter to FTC Chair Lina Khan, Mr. Biden alleged that there is “mounting evidence of anti-consumer behavior by oil-and-gas companies.” He said gasoline prices are rising even as the price of unfinished gasoline goes down.