By Mark Hosenball and Will Dunham

WASHINGTON (Reuters) - The head of the CIA on Friday promised a quick review of whether a Senate report on the agency's use of "enhanced interrogation" methods on foreign terrorism suspects can be released on an unclassified basis, apparently moving to reduce tensions with the CIA's congressional overseers.

CIA Director John Brennan's statement, contained in a message distributed to CIA employees, comes amid a fierce dispute over whether members of the spy agency secretly monitored a Senate Intelligence Committee investigation of the detention and interrogation policies used under former Republican President George W. Bush.

In the message, Brennan praised committee chairwoman Dianne Feinstein, who on March 11 accused the CIA of spying on Congress and possibly breaking the law.

Feinstein, a Democrat, said the CIA had searched computers used by committee staffers examining CIA documents when researching the agency's counterterrorism operations and its use of interrogation methods such as simulated drowning, or "waterboarding."

Brennan, in a message made available to Reuters by a U.S. official, said that Feinstein and the other leaders of the two congressional intelligence panels "carry out their oversight responsibilities with great dedication and patriotism."

He added that "the CIA has benefited over the years from their leadership as well as their strong support for CIA programs and employees."

"I expect the Committee will submit at least some portion of the report to the CIA for classification review, and, if that happens, CIA will carry out the review expeditiously. As I noted in a letter to the Committee last June, CIA must learn from the past and take immediate steps to prevent any shortcomings in Agency intelligence activities," Brennan added.

Senate Majority Leader Harry Reid on Thursday backed Feinstein in the dispute with the CIA, ordering an investigation into what he called an "indefensible" breach of the panel's computers by the CIA.

Story continues

The Senate Intelligence Committee's 6,000-page draft report on the interrogation program was finished more than a year ago but is still classified. Sources say it strongly condemns the now-abandoned harsh interrogation techniques that critics say is torture and concludes that these methods did not produce significant counterterrorism breakthroughs.

The CIA's inspector general has sent the Justice Department a "crimes report" about allegations that the agency had intruded into a computer network that was supposed to be exclusively reserved for Senate investigators. The allegations suggested that the CIA did this in an apparent attempt to learn how the congressional investigators got access to documents that the agency deemed to be covered by legal privilege.

Meanwhile, the agency's acting general counsel sent a second "crimes report" to the Justice Department asking it to look into whether Senate investigators somehow obtained inappropriate access, via CIA networks, to the same documents.

The committee's investigation also has examined the CIA's operation of a network of secret prisons overseas and its use of "rendition," or extrajudicial transfers, of prisoners between countries.

In his message to CIA employees, Brennan said, "In the meantime, you can be sure that we and the Committee are committed to finding a way forward that allows CIA to continue with its important intelligence mission and that promotes effective and independent Congressional oversight of our Nation's classified intelligence activities."

(Reporting by Mark Hosenball and Will Dunham; Editing by Lisa Shumaker)