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CIA Director John Brennan told NBC News' Andrea Mitchell that the agency did not snoop on Senate Intelligence Committee computers to thwart an investigation into illegal detention and interrogations under President George W. Bush.

"We weren't trying to block anything," Brennan said. "The matter is being dealt with in an appropriate way, being looked at by the right authorities, and the facts will come out," he added.

"But let me assure you the CIA was in no way spying on [the committee] or the Senate."

The exclusive Tuesday interview was Brennan's first since the head of the Senate Intelligence Committee charged that the CIA had searched the panel's computers, possibly violating the law.

"The CIA just went and searched the committee's computers," California Democrat Sen. Dianne Feinstein said in a lengthy speech on the Senate floor, calling the the matter a "defining moment" for the oversight of the Intelligence Committee.

"I have grave concerns that the CIA's search may well have violated the separation of powers principles embodied by the United States Constitution, including the speech and debate clause," she said.

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"It may have undermined the Constitutional framework essential to effective congressional oversight of intelligence activity or any other government function."

Feinstein added that the search may also have violated the Fourth Amendment of the Constitution, the Computer Fraud and Abuse Act and an executive order that prohibits the CIA from conducting domestic searches or surveillance.

She said she has asked for an apology and an acknowledgment that the CIA's actions were wrong but that "I have received neither."

The Intelligence Committee is investigating CIA detention and interrogation practices that date back to when Brennan was directing that program.

WATCH: Sen. Dianne Feinstein accuses CIA of spying on Intelligence Commitee

Asked about Feinstein's allegations, White House Press Secretary Jay Carney would not comment on whether the CIA broke any laws but said that "the president has great confidence in John Brennan, and confidence in our inteligence community and in our professionals at the CIA."

Brennan said that he had not seen Feinstein's speech but was aware of "all sorts of claims out there" that the CIA was meddling in the Senate investigation.

"That is not the case at all," he said.

"We greatly respect the separation of powers between the executive branch and the legislative branch," he added.

CIA director denies hacking Senate intel computers to thwart investigation into illegal detention and interrogations under Bush more #AMR - Andrea Mitchell (@mitchellreports) March 11, 2014

Feinstein said the CIA's inspector general turned the matter over to the Justice Department, but Sen. John McCain said an independent probe may be necessary.

After the interview, in a discussion with the Council on Foreign Relations, Brennan said that he supported any effort to ferret out wrongdoing with respect to commitee computers.

"I will be the first one to say we need to get to the bottom of it," he said. "And if I did something wrong, I will go to the president and I will explain to him exactly what I did and what the findings were. And he is the one who can ask me to stay or to go."