WASHINGTON — President Obama said in an interview broadcast on Sunday that while Hillary Clinton had been careless in managing her emails as secretary of state, she would never intentionally do anything to endanger the country.

In his first interview as president with “Fox News Sunday,” Mr. Obama also forcefully vowed that his administration would not interfere with the F.B.I.’s investigation into Mrs. Clinton’s use of a private email server.

“I guarantee that there is no political influence in any investigation conducted by the Justice Department, or the F.B.I. — not just in this case, but in any case,” Mr. Obama told Chris Wallace, the show’s host. “Full stop. Period.”

In October, Mr. Obama drew criticism from some in the Justice Department after he said during a “60 Minutes” interview that Mrs. Clinton’s use of the personal email server did not pose a national security problem. Some F.B.I. officials said the president sounded like he was prejudging the outcome of their investigation.