CHAPEL HILL, N.C. — President Obama threw the power of the White House behind Hillary Clinton on Wednesday. He faulted how the F.B.I. director, James B. Comey, handled new emails related to the investigation into Mrs. Clinton’s private server, and then shouted out to college students here in a pivotal battleground state that it was crucial that they vote because the “fate of the world is teetering.”

Mr. Obama’s comments about Mr. Comey, broadcast early in the day as recent polls showed a tightening race, were striking for a president who has insisted he does not comment on F.B.I. investigations. But Mr. Obama appeared to be doing exactly that in implicitly criticizing Mr. Comey’s decision to send a vague letter last week to Congress — and by extension, the public — informing lawmakers about a discovery of new emails related to Mrs. Clinton’s use of a private server as secretary of state.

“We don’t operate on incomplete information,” Mr. Obama said in an interview with NowThis News. “We don’t operate on leaks. We operate based on concrete decisions that are made.”

Without mentioning Mr. Comey by name — although it was clear whom he meant — Mr. Obama suggested that the F.B.I. had violated investigative guidelines and trafficked in innuendo by alerting Congress last week. Mr. Obama’s remarks, which followed searing criticism of the F.B.I. director from both parties, make it harder for Mr. Comey to defuse the worst crisis of his tenure at the bureau.

The president’s stop later in the day in this liberal college community was aimed at galvanizing two pillars of his political coalition, African-Americans and young voters, who Democrats say are not turning out to vote in the same numbers as they once did for Mr. Obama. If Donald J. Trump loses here and in Florida, where Mr. Obama was heading on Thursday, he has virtually no path to the White House.

“You, North Carolina, are going to have to make sure that we push it in the right direction,” Mr. Obama exhorted about 16,000 cheering supporters at the University of North Carolina. It was Mr. Obama’s second stop on a weeklong swing through four pivotal states and demonstrated a new level of urgency among Democrats about the race as well as the personal stakes for Mr. Obama, who wants Mrs. Clinton to carry on his agenda.

After saying for a second time that “the fate of the republic” rested on their shoulders, Mr. Obama made sure to add he was not joking. His language, here and in the interview, reflected how determined he was to defeat Mr. Trump and betrayed how nervous some in his own party have become over Mrs. Clinton’s prospects.

The president also lashed out at Republicans for vowing to create gridlock in Washington if Mrs. Clinton is elected, saying that “you’ve got some Republicans in Congress who are already suggesting they will impeach Hillary. She hasn’t even been elected yet.”

In Washington, Mr. Obama’s criticism of Mr. Comey was only the latest blow to the F.B.I., where the mood is grim as agents continue to review emails belonging to Huma Abedin, a top aide to Mrs. Clinton. The emails were discovered in an unrelated investigation into her estranged husband, Anthony D. Weiner, a former congressman from New York. The F.B.I. is investigating whether Mr. Weiner sent illicit text messages to a teenage girl in North Carolina and seized his laptop in early October.

The F.B.I. concluded the case into Mrs. Clinton’s private server in July with no charges, but Mr. Comey’s letter to Congress has renewed an inquiry that Mrs. Clinton thought was behind her.

For Mr. Comey, the short time left before the election now offers no easy options. If, over the next few days, agents find no evidence to change their July conclusion in the emails of Ms. Abedin that they are able to review — law enforcement officials say the F.B.I. likely will not be able to complete the inquiry by Tuesday — publicly saying so would open the F.B.I to criticism that it was prejudging an open investigation.

If agents do find potentially damaging evidence, publicly saying so would taint Ms. Abedin — and by extension Mrs. Clinton — before the investigation is complete. Either move would amount to a change in practice for the F.B.I., which typically says only what it believes it can prove, and only in court

“The risk of harm is greater if he comes out without all the facts,” Chris Voss, a former F.B.I. agent, said of Mr. Comey.

Saying nothing, however, allows suspicion to hang over Mrs. Clinton’s campaign in the final days of the race. Mr. Trump has already capitalized on the F.B.I. review at his rallies, calling it evidence of what he calls Mrs. Clinton’s corrupt and criminal behavior.

Mr. Comey’s letter has also put Mr. Obama into a delicate position at a crucial time in the race, essentially forcing him to choose between his own institutional imperative to refrain from meddling in a federal law enforcement matter and his political impulse to fiercely defend Mrs. Clinton.

White House officials later played down Mr. Obama’s remarks about the F.B.I. and insisted he had not meant to criticize Mr. Comey.

“The president went out of his way to say he wouldn’t comment on any particular investigations,” Eric Schultz, a White House spokesman, told reporters on Air Force One while Mr. Obama was en route to North Carolina.