WASHINGTON — More than a year after Republican leaders promised to investigate Russian interference in the presidential election, two influential Republicans on Friday made the first known congressional criminal referral in connection with the meddling — against one of the people who sought to expose it.

Senator Charles E. Grassley of Iowa, the chairman of the Judiciary Committee, and Senator Lindsey Graham of South Carolina, a senior committee member, told the Justice Department that they had reason to believe that a former British spy, Christopher Steele, lied to federal authorities about his contacts with reporters regarding information in a dossier, and they urged the department to investigate. The committee is running one of three congressional investigations into Russian election meddling, and its inquiry has come to focus on, in part, Mr. Steele’s explosive dossier that purported to detail Russia’s interference and the Trump campaign’s complicity.

The decision by Mr. Grassley and Mr. Graham to single out the former intelligence officer behind the dossier infuriated Democrats and raised the stakes in the growing partisan battle over the investigations into Mr. Trump, his campaign team and Russia.

The Senate Judiciary Committee effort played into a far broader campaign waged by conservatives to cast doubt on the Trump-Russia investigations, and instead turn the veracity of the dossier and the credibility of its promulgators into the central issue. At the same time, President Trump and his allies have demanded that the Justice Department reopen its investigation of Hillary Clinton’s email server and the Clinton Foundation. F.B.I. agents have begun interviewing people connected to the foundation about whether any donations were made in exchange for political favors while Mrs. Clinton was secretary of state.