The CIA denied hacking into the Senate's computers or that it was trying to thwart the investigation into the torture programme, with John Brennan, the director, saying "nothing could be further from the truth".
Brennan told NBC News: "The matter is being dealt with in an appropriate way ..."
The confrontation stems from Feinstein's effort to compile a comprehensive and public account of the CIA torture programme carried out at Guantanamo Bay and "black site" prisons around the world following the September 11 attacks.
The programme, which included simulated drowning and the subcontracting out of torture to foreign spy agencies, was ordered by the Bush Administration but halted when President Barack Obama took office in 2009.
Although the CIA has fought to keep details of the programme secret, it agreed to hand over 6.2 million documents to the staff of the Senate intelligence committee and create a secure network for the documents to be searched.
Feinstein said that among those files was an "especially significant" internal CIA review document on the torture programme.
The review, which was never intended to be seen outside the CIA, contradicted claims that the agency was making in official submissions to the Senate.
"That's what makes [it] so significant and important to protect," Feinstein said.
The CIA claims that it never handed over the internal review and that Senate investigators must have obtained it by illicit means.
In an effort to figure out where it had come from they broke into the Senate's secure network and began deleting files, Feinstein claimed.
"The CIA did not ask the committee or its staff if the committee had access to the internal review, or how we obtained it," she said. "Instead, the CIA just went and searched the committee's computers."
The CIA even approached the Department of Justice and accused the Senate staff of breaking the law.
"There is no legitimate reason to allege to the Justice Department that Senate staff may have committed a crime," Feinstein said, calling the move "a potential effort to intimidate this staff - and I am not taking it lightly".
Feinstein said that she made the allegations "reluctantly" and only after exhausting private channels for resolving the conflict. She is now pushing to declassify portions of her committee's report into the CIA torture programme.
The White House supports declassification but it must first pass a vote of the Senate's 15-member intelligence committee.
"If the Senate can declassify this report, we will be able to ensure that an un-American, brutal programme of detention and interrogation will never again be considered or permitted," she said.