The pilot of a private plane that was chased by fighter jets before crashing in Virginia was seen slumped over in the cockpit, US media report.

Fighter jets spotted the seemingly unconscious pilot after intercepting the aircraft, officials told outlets including the Washington Post and CNN.

The pilot and three other passengers died in Sunday's crash.

The Cessna Citation aircraft crossed restricted airspace over Washington DC before plummeting in Virginia.

The plane, which had been heading to Long Island from Tennessee, made a hairpin turn when it reached New York before flying back south towards its origin.

When it entered airspace over the US capital, some of the most restricted in the country, F-16 fighter jets were permitted to fly at supersonic speed to intercept it and a loud sonic boom reverberated around the region.

The pilot was silent for the last two hours of the flight and the aircraft ultimately ran out of fuel and crashed in a densely wooded, mountainous area near Montebello in Virginia.

It is not clear why the pilot was unresponsive. Military officials speaking on condition of anonymity said the plane was not shot down and fighter jets did not cause the crash.

Investigators are now combing through rural Virginia assessing the wreckage which is said to be "highly fragmented". That operation is likely to take days, officials said.

"Everything is on the table until we slowly and methodically remove different components and elements that will be relevant for this safety investigation," National Transportation Safety Board investigator Adam Gerhardt said.

A report with further details will be released next week. A final report on the fatal incident will be released in 12 to 24 months.

The four people who died have not been formally identified, but a person linked to the plane said his family members were onboard.

John Rumpel, 75, who runs the Florida business that owned the aircraft, told the New York Times his daughter, two-year-old granddaughter and her nanny were on the plane along with the pilot.

He said they had been returning to East Hampton, New York state, from his North Carolina home.

"It descended at 20,000ft a minute, and nobody could survive a crash from that speed," Mr Rumpel, who is also a pilot, said, adding that he hoped his relatives had not suffered.

Mr Rumpel, speaking separately to the Washington Post, identified the pilot as Jeff Hefner who he said had been flying for more than five years. He has not been named by officials.

Richard Levy, a retired captain and pilot instructor, told BBC News that the Cessna probably lost cabin pressure.

Aircraft cabins can depressurise for a number of reasons, including because of aircraft mechanical malfunctions or pilot errors, he said.

In this case, Mr Levy said the cabin may have depressurised gradually and "insidiously" without those on board even noticing symptoms of hypoxia - a condition in which the body is deprived of adequate levels of oxygen - until it was too late.

"They're unaware of what's happening, and then they've gone beyond the point of rational thinking, consciousness and good vision," Mr Levy said.

Mr Levy said the pilot may have realised at one point that the cabin was depressurising and then tried to turn the aircraft around on an autopilot setting. "After that, my assumption is that the pilot then lost consciousness," he said.