After he took office, senior F.B.I. counterintelligence agents met with Ms. Hicks in the White House Situation Room at least twice, gave her the names of the Russians who had contacted her, and said that they were not who they claimed to be. The F.B.I. was concerned that the emails to Ms. Hicks may have been part of a Russian intelligence operation, and they urged Ms. Hicks to be cautious.

The meetings with Ms. Hicks, what the F.B.I. calls a “defensive briefing,” went beyond the standard security advice that senior White House officials routinely receive upon taking office. Defensive briefings are intended to warn government officials about specific concerns or risks. A lawyer for Ms. Hicks declined to comment.

The contents of the emails to Ms. Hicks are unclear, as are the identities of the Russians who sent them. The people who described the briefing and the emails spoke on the condition of anonymity because they were not authorized to openly discuss intelligence matters. The F.B.I. declined to comment.

On Thursday and Friday, investigators working for Robert S. Mueller III, the special counsel, interviewed Ms. Hicks as part of his investigation into Russia’s efforts to influence the 2016 election and whether any of Mr. Trump’s advisers assisted the Russian campaign. It is not clear whether the Russian efforts to contact Ms. Hicks were discussed during that interview.

In early January, American intelligence agencies formally accused Russian intelligence agencies of trying to tip the presidential election toward Mr. Trump, who was reluctant to accept that conclusion. Against that backdrop, senior F.B.I. officials went to the White House in the early days of the Trump administration and warned all senior aides to be cautious about espionage threats, especially from Russia and China.