(Reuters) - Republican leaders in the U.S. Congress have refused Democrats’ calls for a special prosecutor or select committee to investigate Russian meddling in the 2016 presidential election, including possible links between President Donald Trump’s campaign and Moscow, saying investigations by congressional committees are sufficient. U.S. intelligence agencies said in January that Russian President Vladimir Putin ordered hacking of the Democratic National Committee and the chairman of Hillary Clinton’s Democratic campaign to influence the election on behalf of Trump, a Republican. Russia has denied this. The Central Intelligence Agency, National Security Agency, Federal Bureau of Investigation and the Justice Department all launched investigations under President Barack Obama. Following are some ways Congress is looking into the matter: HOUSE INTELLIGENCE COMMITTEE - The House Permanent Select Committee on Intelligence began its investigation of potential Russian influence on the 2016 presidential race before Trump took office on Jan. 20. The panel’s chairman, Republican Representative Devin Nunes, a close Trump ally, recused himself from the investigation last month. Before he stepped aside, Democrats had questioned whether the committee could conduct a credible investigation after Nunes received information at the White House about surveillance and discussed it with Trump before briefing Democrats on the committee. Nunes was replaced as leader of the House investigation by Republican Representative Mike Conaway, an intelligence panel member. The committee held a high-profile public hearing on March 20 with testimony by FBI Director James Comey and NSA director Admiral Mike Rogers. But Nunes canceled another planned public hearing with former Obama administration officials James Clapper, who was director of national intelligence, former Deputy Attorney General Sally Yates and ex-CIA Director James Brennan, causing committee Democrats to accuse him of political motivations. The two parties reached a solution last week, announcing a closed hearing with Comey and Rogers for May 2, and a public one with the Obama administration officials for an as-yet-to-be-determined date. SENATE INTELLIGENCE COMMITTEE - The U.S. Senate Select Committee on Intelligence is conducting its own investigation, which also started before Trump took office. Staffers have begun interviewing intelligence analysts involved in the report announced in January that charged Russia with seeking to influence the election on Trump’s behalf. Its chairman, Senator Richard Burr, was re-elected in November in the Republican sweep that carried Trump into office and preserved Republican control of Congress. He and Senator Mark Warner, the committee’s Democratic vice chairman, have pledged that their investigation would be bipartisan despite questions over Burr’s close ties to the White House. But far fewer staff members have been assigned to the panel’s investigation than previous high-profile intelligence probes in Congress, according to sources and a Reuters review of public records. SENATE JUDICIARY COMMITTEE - Republican Senator Lindsey Graham, chairman of the panel’s subcommittee on crime and terrorism, and Sheldon Whitehouse, the subcommittee’s ranking Democrat, are looking into Russian attempts to influence the election. The subcommittee announced on Tuesday that it would hold a public hearing on May 8 with testimony by Yates and Clapper. Its chairman of the full Judiciary Committee, Chuck Grassley, and top Democrat Dianne Feinstein also have had officials brief panel members.     SENATE APPROPRIATIONS COMMITTEE - The Appropriations subcommittee that oversees U.S. government spending for the State Department, which is also chaired by Senator Graham, has also held hearings on Russian attempts to influence elections. HOUSE OVERSIGHT COMMITTEE - Representative Jason Chaffetz, the committee’s Republican chairman, has resisted calls to investigate the Trump administration. But he and Representative Elijah Cummings, the top Democrat on the committee, said on Tuesday Trump’s former national security adviser Michael Flynn likely broke the law by failing to get permission to be paid for a trip to Russia in 2015. Chaffetz announced last week that he would not run for re-election in 2018, and said he might leave office even before the end of his term. 