“The C.I.A did not file any report on Snowden indicating that it suspected he was trying to break into classified computer files to which he did not have authorized access while he was employed at the C.I.A., nor was he returned home from an overseas assignment because of such concerns,” Todd Ebitz, an agency spokesman, said in the statement.

In dispute is what Mr. Snowden did on his computer, and the agency’s response to it. The two officials cited by The Times said the C.I.A. suspected Mr. Snowden was trying to gain access to classified computer files he was not authorized to view. But other officials on Friday characterized the activity as much less serious, not involving potential security violations.

It was unclear why there was a divergence of opinion.

These officials on Friday also said that Mr. Snowden left the C.I.A. of his own volition. But had he remained with the agency in Geneva, they said, Mr. Snowden faced a potentially time-consuming and critical internal inquiry prompted by his supervisor’s report, an investigation that was halted once he quit the C.I.A. in 2009 to join the N.S.A. as a contract employee at a military facility in Japan.

In his statement, Mr. Ebitz did not dispute the existence of the supervisor’s derogatory report or its mention of a disturbing shift in Mr. Snowden’s behavior as he was preparing to leave the agency he had joined in 2006 for a new job as a contractor for the National Security Agency. He also did not dispute that the supervisor’s cautionary note was not forwarded to the N.S.A. or its contractors, and surfaced only after federal investigators began scrutinizing Mr. Snowden’s record once the documents began spilling out.