WASHINGTON — The Obama administration has asked Congress to give clear authority to the Federal Bureau of Investigation to obtain records related to the context of e-mails and other Internet-based communications without first obtaining a warrant from a judge.

Some advocates of electronic privacy have raised alarms about the proposal, saying it could expand government eavesdropping on computer activity without court oversight. Senator Patrick J. Leahy, Democrat of Vermont and chairman of the Senate Judiciary Committee, said Thursday that the proposal raised “serious privacy and civil liberties concerns.”

The administration portrays its proposal, first reported by The Washington Post, as a mere technical fix to clarify a confusingly written statute and...