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White House Chief of Staff Denis McDonough and White House Counsel Kathryn Ruemmler met with Sen. Dianne Feinstein late Tuesday to try to deescalate the dispute between the Senate Intelligence Committee and the CIA, NBC News has learned.

The pair met with Feinstein, D-Calif., before a lengthy intelligence panel meeting.

In his first comments on the controversy, President Barack Obama urged the Senate Wednesday to complete its report on past CIA interrogation practices as soon as possible. But Obama would not weigh in on the dispute itself because the matter is under investigation.

White House spokesman Jay Carney confirmed that CIA Director John Brennan and the CIA's acting general counsel both referred the Senate's treatment of classified documents to the Justice Department for a possible criminal investigation.

Feinstein says that referral is merely an attempt to intimidate the intelligence committee’s staff, whom she claims was acting appropriately. The California Democrat was particularly incensed because the CIA lawyer who asked for the criminal investigation was himself the subject of the probe into interrogation practices.

Feinstein argues that the Senate had the legal right to control CIA data in secure computers during its investigation into past abuses by the CIA under President George W. Bush - as part of a prior agreement signed by former CIA Director Leon Panetta.

Brennan argues that those computers are technically part of the CIA's data system and are not legally the Senate's, meaning that the CIA search of the computers was not "spying."