Republicans and Democrats sternly warned the FBI on Tuesday that it could lose its broad power to collect telephone, e-mail and financial records to hunt terrorists after revelations of widespread abuses of the authority detailed in a recent internal investigation.

Their threats came as the Justice Department’s chief watchdog, Glenn A. Fine, told the House Judiciary Committee that the FBI engaged in widespread and serious misuse of its authority in illegally collecting the information from Americans and foreigners through so-called national security letters.