By contrast, Mr. Trump said late last month that he had not brought up the suspected operation when he spoke with President Vladimir V. Putin of Russia, dismissing it as “an issue that many people said was fake news.” Russian officials have denied the accusations.
Mr. Pompeo provided few details about the warnings. He did not, for example, say whether it was a vague and abstract warning or threatened specific consequences. He also did not specify who had delivered the Pentagon’s message and to whom, or when.
However, a rare channel of direct, high-level communication between the two militaries involves Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, who spoke with his Russian counterpart, Gen. Valery Gerasimov, six weeks ago, shortly after The New York Times first reported on the C.I.A. assessment.
Asked whether General Milley raised bounties with General Gerasimov, Pentagon officials have responded by insisting that such conversations remain private so that the two men can maintain close contacts for use in times of strife.
Mr. Pompeo also did not say when he had warned Mr. Lavrov, but his remarks confirmed a New York Times report last week that he delivered such a message in a July 13 call, according to people briefed on the matter. They said Mr. Pompeo had couched the warning as a hypothetical, even as he implied that he was referring to the reports about the C.I.A.’s assessment on Russian bounties in Afghanistan.