“There’s a debate among national security experts, as part of their ongoing, independent review, about how or even whether to classify sections of those emails,” said Josh Earnest, the White House press secretary. “But, as the president said, there is no evidence to indicate that the information in those emails endangered our national security.”

Whether Mr. Obama’s remarks have a lasting effect beyond upsetting some F.B.I. officials depends on the investigation’s outcome.

Since the email inquiry began this past summer, investigators have been scrutinizing everyone who came in contact with Mrs. Clinton’s server and trying to determine whether anyone sent or received classified information, whether that information was compromised and whether any of this amounted to a crime.

Tensions among career F.B.I. agents, the political appointees who run the Justice Department and the White House are commonplace. In deciding whether to bring charges in a case, F.B.I. agents are often more bullish. Prosecutors, with an eye toward trying to win at trial, tend to be more cautious and have the final say. As such, no administration, Democratic or Republican, is immune from the suspicion that politics has influenced case decisions.

But Mr. Obama’s remarks in the Clinton email case were met with particular anger at the F.B.I. because they echoed comments he made in 2012, shortly after it was revealed that a former C.I.A. director, David H. Petraeus, was under investigation, accused of providing classified information to a mistress who was writing a book about him.

“I have no evidence at this point, from what I’ve seen, that classified information was disclosed that in any way would have had a negative impact on our national security,” the president said at a 2012 news conference, as the F.B.I. was trying to answer that very question about Mr. Petraeus.

At the time, the Obama administration was leading a historic crackdown on government officials who discussed national security matters with reporters, even when that information was never disclosed publicly. But Mr. Petraeus was a four-star general, a White House adviser and the most celebrated military leader of his generation. F.B.I. officials were concerned that he would receive preferential treatment.