A loud noise that was heard across much of the Washington, D.C., area on Sunday afternoon was caused by the sonic boom from military jets scrambling to respond to an intrusion into restricted airspace by a private flight, military and U.S. officials confirmed on Sunday.

Two fighter jets were sent from Joint Base Andrews after a Cessna entered the restricted airspace, prompting the emergency response to intercept the flight, the officials confirmed on Sunday. The private aircraft’s owner said in a telephone interview that four people, including his daughter and granddaughter, were on the plane and that the wreckage had not yet been found.

The North American Aerospace Defense Command, or NORAD, which oversees aerospace control over the United States and Canada, said in a statement that two F-16 jets were deployed after the Cessna 560 Citation V flew over Washington and Northern Virginia.

NORAD said that the fighter jets “were authorized to travel at supersonic speeds,” which would have produced the boom that was heard in the region and by some reports was noticed as far as the suburbs of Virginia and Maryland. The NORAD aircraft also used flares that may have been visible from the ground, the agency said, “in an attempt to draw attention from the pilot.”

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.”

“I don’t think they’ve found the wreckage yet,” Mr. Rumpel said. “It descended at 20,000 feet a minute, and nobody could survive a crash from that speed.”

The aircraft had taken off from Elizabethton Municipal Airport in Elizabethton, Tenn., and was bound for Long Island MacArthur Airport in Ronkonkoma, N.Y., the F.A.A. said, adding that the incident was under investigation. The Cessna Citation bound for the Long Island airport left Tennessee at 1:13 p.m., according to the flight tracking website FlightAware.

The Annapolis Office of Emergency Management had also said on Twitter that the sonic boom resulted from an authorized Defense Department flight.

Shortly after the incident, people reported on social media that they had heard a loud boom in Washington, as well as in Maryland and Northern Virginia. Many said the noise sounded like an explosion, and some said the boom was so strong that it shook their homes. A sonic boom is caused by an object moving faster than sound, or about 750 miles per hour at sea level.

The noise from the sonic boom startled people across the Washington area, and many took to social media to speculate about what could have caused it.

Rafael Olivieri, 62, said he was at home in Annandale, Va., when he heard a “loud, very short sound” that shook his house. Mr. Olivieri ran outside, where his neighbors were also trying to figure out what had happened. “My first thing was looking to the sky,” he said. “I was really worried.”

More than 30 miles northeast, in Edgewater, Md., Joseph Krygiel, 47, also felt the boom. He said he was in his basement just after 3 p.m. when the whole house shook. “It felt like something major,” Mr. Krygiel said.

Washington’s Homeland Security and Emergency Management Agency also acknowledged the boom.

“We are aware of reports from communities throughout the National Capital Region of a loud ‘boom’ this afternoon,” the agency said on Twitter. “There is no threat at this time.”