WASHINGTON—The private company that conducted the last background check of former National Security Agency contractor Edward Snowden said it was the federal government's responsibility to catch any problems with its 2011 investigation of the man who has said he leaked top-secret documents.

US Investigations Services LLC defended its work after a review by the Office of the Director of National Intelligence concluded that the Falls Church, Va.-based company conducted an inadequate examination of Mr. Snowden for the renewal of...