WASHINGTON—A federal judge rejected a request from an insurance-industry group to block a new rule on retirement advice, handing an early victory to the Obama administration in its defense of the landmark regulation against a series of legal challenges.

Friday’s ruling by the U.S. District Court in Washington involved a case filed by the National Association for Fixed Annuities, or NAFA, which asked for a court order to place the rule’s implementation on hold.

The...