Testifying behind closed doors on Capitol Hill in late March, the official, John K. Mashburn, said he remembered the email coming from George Papadopoulos, a foreign policy adviser to the campaign who was approached by a Russian agent, sometime before the party conventions — and well before WikiLeaks began publishing messages stolen in hackings from Democrats.

Such an email could have proved explosive, providing evidence that at least one high-ranking Trump campaign official was alerted to Russia’s meddling, raising questions about which advisers knew and undercutting President Trump’s denials of collusion.

But two months after Mr. Mashburn testified, investigators for the Senate Judiciary Committee have not found any such message. The special counsel, Robert S. Mueller III, was also searching for similar emails, according to a person familiar with a request for documents that his investigators sent to the Trump campaign. The campaign, which has examined its emails and other documents, also cannot find the message, and officials do not believe it exists.