The Justice Department said on Friday it will seek a court order to force Apple Inc. to help unlock an iPhone seized as part of a New York drug investigation, another sign the fight between Washington and Silicon Valley over encryption is far from over.

Apple’s lawyers fired back that they intend to press the federal prosecutors to explain exactly why they can’t get into the iPhone on their own and want the names of any companies that are helping with the effort, citing the recent announcement by the Federal Bureau of Investigation...