The U.S. Justice Department took the unusual step of suing Barclays PLC, alleging the bank fraudulently sold more than $30 billion of mortgage securities that helped fuel the financial crisis, after long-running settlement negotiations broke down.

The complaint filed Thursday against the U.K.’s second-largest bank shows the urgency among senior Obama appointees in the Justice Department to resolve the outstanding probes of precrisis conduct at major banks before those officials leave office in mid-January. Part of the urgency...