Judge Amit P. Mehta said Google must hand over some of its search data to rivals, falling short of the sweeping changes proposed by the government to rein in the power of Silicon Valley.

In a landmark antitrust case, the Justice Department asked a federal judge to force the company to sell its popular Chrome browser. The Department of Justice and a group of states had until the end of Wednesday to propose remedies in an antitrust lawsuit they won in August.