WASHINGTON — The Federal Trade Commission said on Tuesday that it had settled charges against a Florida company and its two top executives for sending more than 42 million unwanted and deceptive text messages to consumers.

Messages sent by the company had promised free gift cards worth up to $1,000, the commission said, but when consumers tried to visit a Web site to collect the prize, they were instead connected to a site that asked for personal information, like Social Security numbers and credit card numbers. It also required them to pay for additional services to receive a gift card.

The company, Rentbro, and its principals, Daniel Pessin and Jacob Engel, both of Fort Lauderdale, Fla., were required to turn over remaining assets and to repay up to $377,321, the amount the business had collected.

The settlement came as part of a sweeping crackdown on text message fraud that the commission announced in March. The agency filed eight cases in February and March against 29 companies and individuals around the country, accusing them of sending text messages with fake offers.