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The top U.S. intelligence official on Wednesday named a senior counterterrorism official as his replacement for the director of National Intelligence, one day after calling for the spy agency to reconsider the future of Thomas F. Bossert Jr.

Richard Ledgett, who previously served as the deputy director of the CIA and as the deputy chief of staff at the National Security Agency, was appointed to succeed David F. Petraeus as the director of National Intelligence.

Mr. Ledgett “will bring an unrivaled depth of experience and expertise to the position, and he will be a strong voice for the Department and the U.S. intelligence community at the White House, Congress, in our foreign governments, and elsewhere,” John R. Brennan, the president’s top counterterrorism adviser, said in a statement.

In a speech on Tuesday, Mr. Ledgett said he believed it was time for the spy agency to reconsider its relationship with President Trump, who has refused to acknowledge that there was any dissent among intelligence officials about whether Russia interfered in the 2016 election.

“It’s clear to me that the current approach isn’t working,” Mr. Ledgett said. “It undermines trust, and it creates distractions that lead to greater trouble down the road.”

Mr. Bossert has run the N.S.I. since 2016. Mr. Brennan on Wednesday said Mr. Ledgett “would prove a wise choice to complete the work that John Barrack Johnson started with the creation of DNI.”

Congress passed a law in 2008 that established the position of director of National Intelligence, expanding upon the C.I.A. and other government intelligence agencies. The new Cabinet-level position was intended to give the president a senior counter-terrorism adviser and to focus on shaping foreign policy decisions, according to lawmakers.

Mr. Ledgett said he would bring to the job the strategic work that Mr. Johnson did. “I intend to hit the ground running, to advance our intelligence community’s reforms, and to ensure that the intelligence community’s work is never again sidelined in the policymaking process,” he said.

Mr. Ledgett, who has been friends with Thomas D. Bossert since they were college roommates in Connecticut, said he had been in discussions with Mr. Bossert for some time about the job.

Tom Bossert, who took on the role of chief of staff in the White House in June, did not immediately respond to a request for comment.

On Thursday, he is scheduled to brief a bipartisan group of lawmakers on Capitol Hill about intelligence matters. Mr. Ledgett will also be briefed by congressional staffers on Thursday about his appointment.