By Patricia Zengerle

WASHINGTON, March 13 (Reuters) - U.S. Republican congressional leaders have refused Democrats' calls for a special prosecutor or select committee to investigate possible links between President Donald Trump's campaign and Russia, saying investigations by congressional committees are sufficient.

U.S. intelligence agencies said in January that Russian President Vladimir Putin had ordered hacks of the Democratic National Committee's and Hillary Clinton's campaign chairman's computers to influence the election on Trump's behalf.

Russia has denied this.

Three U.S. agencies - the CIA, the National Security Agency and the Federal Bureau of Investigation - as well as the Justice Department, launched investigations into the matter under Democratic President Barack Obama.

In addition, here are some of the ways that congressional committees are 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, played a leading role in Trump's transition, which prompted some critics to question whether he was too close to the Republican president to conduct a fair investigation.

Some of Nunes' statements contributed to their concerns, including his confirmation that he had spoken to journalists at the White House's request to dispute reports that Trump's campaign had contact with Russia.

Nunes has also said he does not want the investigation to turn into a "witch hunt" like the 1950s McCarthy congressional hearings into some Americans' alleged links with communism.

The committee members had to push for full access to information collected by the CIA, FBI and other agencies, but more recently they have said their access has improved.

The panel will hold its first public hearing on the matter on March 20. FBI director James Comey and the leaders or former leaders of most of the major U.S. intelligence agencies have been invited to testify.

Representative Adam Schiff, the top Democrat on the committee, said he does not know yet whether the panel is capable of conducting a credible investigation.

SENATE INTELLIGENCE COMMITTEE - The U.S. Senate Select Committee on Intelligence is conducting its own investigation. Also started before Trump took office, it is considered the most robust congressional action.

Its chairman, Richard Burr, was re-elected in November in the Republican sweep that carried Trump into office and preserved Republican control of Congress. Although he was a Trump supporter during the campaign, he is not as closely linked with the president as Nunes is. But he also made calls to reporters as the White House tried to dispute allegations about campaign contacts with Russia.

Senator Mark Warner, the committee's Democratic vice chairman, said he had "grave concerns" about the independence of the committee's probe after the report that Burr had helped the White House dispute the stories.

Burr and Warner have expressed fewer concerns than members of the House committee about the amount of information that intelligence agencies have provided to them.

The Senate committee has not yet scheduled any public hearings on the matter.

SENATE JUDICIARY COMMITTEE - Republican Senator Lindsey Graham, chairman of the panel's subcommittee on crime and terrorism, and Sheldon Whitehouse, its ranking Democrat, announced that they, too, would investigate Russian attempts to influence the election.

They also have asked the FBI and the Justice Department to produce any information that supports Trump's unsubstantiated claim that his predecessor wiretapped him during the 2016 campaign.

The full Judiciary Committee is also investigating. Its chairman, Chuck Grassley, and top Democrat, Dianne Feinstein, have had officials brief panel members.

Grassley and Feinstein also sent a joint letter to Comey asking for a briefing and transcripts and documents of calls between Michael Flynn, Trump's former national security adviser, and Russian Ambassador Sergei Kislyak.

HOUSE JUDICIARY COMMITTEE - Committee Democrats tried to force the committee to ask the Department of Justice to produce records of its investigation into whether Trump or his campaign had ties to Russia, but panel Republicans blocked the effort.

The committee's chairman, Representative Bob Goodlatte, said instead that he would urge the government to continue its investigation.

However, Goodlatte said he had asked the Justice Department to brief the committee, and had not had a response.

HOUSE OVERSIGHT COMMITTEE - Jason Chaffetz, the committee's Republican chairman, has resisted calls to investigate the Trump administration. After Michael Flynn resigned as Trump's national security adviser because of his calls to Russia's ambassador, Chaffetz said his panel would not look into the issue.

He has, however, signed letters seeking related information, and he was among the first lawmakers to call for Attorney General Jeff Sessions to recuse himself from Russia-related investigations because of his contacts with Kislyak. (Reporting by Patricia Zengerle; Editing by John Walcott and Jonathan Oatis)

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