WASHINGTON — A top congressional intelligence official said on Sunday that American counterintelligence officials are virtually unanimous in believing that Edward J. Snowden is “under the influence of Russian intelligence services.”

That suggestion came from Representative Mike Rogers, the Michigan Republican who is chairman of the Intelligence Committee.

Mr. Rogers had previously raised the possibility that Mr. Snowden, the former National Security Agency contractor, might be working for Russia, though the congressman has yet to offer any evidence. His assertions on Sunday, however, were his most sweeping to date.

“Every counterintelligence official believes that,” Mr. Rogers said on the NBC News program “Meet the Press.” “You won’t find one that doesn’t believe today he’s under the influence of Russian intelligence services.”