The company that conducted a background investigation on the contractor Edward J. Snowden fraudulently signed off on hundreds of thousands of incomplete security checks in recent years, the Justice Department said. The government said the company, U.S. Investigations Services, defrauded the government of millions of dollars by submitting more than 650,000 investigations that had not been completed. The government uses those reports to help make hiring decisions and decide who gets access to national security secrets. In addition to Snowden, the company performed the background check for Aaron Alexis, a 34-year-old military contractor who killed 12 people at the Washington Navy Yard last year. The accusations highlight not just how reliant the government is on contractors to perform national security functions, but also how screening those contractors requires even more contractors. U.S. Investigations Service, now known as USIS, is the largest outside investigator for government security clearances. It is one of many companies that has found lucrative government work during the expansion of national security in the last decade. The government made the accusations in a 25-page complaint filed in United States District Court in Montgomery, Ala., where USIS has been the subject of a whistle-blower lawsuit since 2011. “These allegations relate to a small group of individuals over a specific time period and are inconsistent with the strong service record we have earned since our inception in 1996,” said a spokesman for USIS.