A man set himself on fire near the US Congress on Friday, police said, one day after a woman was shot dead by law enforcement after a high-speed chase nearby.

"It does appear that a man sustained self-inflicted burns," Metropolitan Police Department spokeswoman Gwendolyn Crump said.

"The investigation is still unfolding."

The incident followed dramatic scenes on the streets of the American capital on Thursday, when a 34-year-old woman led police on a high-speed car chase before being shot dead.

Police on Friday raced to the scene at the National Mall grassy esplanade just steps from the US Capitol.

The man was conscious and breathing when police got on the scene around 4:30 pm (2030 GMT), Crump's office said.

Fire and rescue crews on the scene, and Metro Transit Police was assisting with the case.

Washington tourist Meghan Van Heertum, who was standing nearby, said the man was African-American.

She said the man was taken to an ambulance and then airlifted by helicopter.

"There were just a few cops at that time. One of them kicked something that was on fire, about 15 feet (4.5 meters) away from the site," said Van Heertum, 29.

"Somebody extinguished the flames. I saw a cop run to his truck and grab a cooler full of ice, grabbed bottles of water, ran back over.

"There were some guys without their shirts on and I heard from some people that this man had set himself on fire, bystanders took off their shirts to put out the fire.

"It smelled very strong of burnt flesh."

Another bystander, Ellie Hess, took to Twitter to express her shock at the rare incident.

" ... someone just lit himself on fire in the middle of the National Mall," she said, tweeting a picture of police and emergency vehicles rushing to the scene as people watched.