After the Cessna veered into the restricted area, which includes important national landmarks, the Federal Aviation Administration called the pilot but received no response from that plane, and the military ordered the jets to intercept, a military official said.

Officials later determined that the Cessna plane did not pose a threat, and the investigation will look into why the pilot did not respond to the F.A.A. The Cessna was not shot down, the officials said. A White House official said President Biden was briefed on the incident.

The Cessna crashed near the George Washington National Forest in Virginia, NORAD said, though an earlier statement from the F.A.A. said it “crashed into mountainous terrain in a sparsely populated area of southwest Virginia,” near Montebello, around 3:30 p.m. local time. The Virginia State Police said on Sunday evening that search efforts for the wreckage and its passengers were underway near the Blue Ridge Parkway and Staunton, Va.

The condition of those onboard was not yet known.

The aircraft, a private business jet, was owned by Encore Motors of Melbourne, a Florida-based company. Reached by phone, John Rumpel, 75, who runs that company, said that his daughter, a 2-year-old granddaughter, her nanny and the pilot were aboard the flight. He said they were returning home to East Hampton, N.Y., after a four-day visit to his home in North Carolina.

Mr. Rumpel, who is also a pilot, said that he had little information about the circumstances of the crash, but hoped they had not suffered. His voice breaking, he said that if the plane lost pressurization, “they all just would have gone to sleep and never woke up.”