SAN FRANCISCO — A federal judge posed tough questions on Thursday about the adequacy of a proposed $12.25 million settlement between Lyft Inc. and its drivers but held off on ruling.

U.S. District Judge Vince Chhabria of the Northern District of California seemed particularly skeptical that the deal sufficiently compensates the company’s most frequent drivers. The lawsuit claims that all Lyft drivers should be classified as employees—not independent contractors—and are entitled to reimbursement for mileage and other costs back to May 2012.