US police shot a female motorist dead on Thursday after she led them on a wild high-speed chase from the White House through downtown Washington to the Capitol building.

Lawmakers and tourists scattered and ducked for cover as shots rang out during a police operation to halt the woman, who was driving with a one-year-old child in her black Infiniti luxury sedan.

Washington police chief Cathy Lanier told reporters that the suspect had been pronounced dead, but refused to discuss her identity or her possible motive while the investigation was continuing.

"The child is approximately a year old, and is in good condition, and in protective custody," Lanier said, adding that officers had fired shots at two locations as they tried to halt the vehicle.

"I will say that both at the White House and at the Capitol, the security perimeter worked," she said, adding that a Capitol Police officer and a Secret Service agent had been injured.

"They did exactly what they were supposed to do. They stopped a suspect from breaching the security perimeter in a vehicle at both locations," she said.

Officials said that the chase had begun at the "outer perimeter" of White House security, where the suspect's car had struck a barrier and a uniformed Secret Service officer.

No shots were fired at the White House, but agents gave chase. As the car closed in on the Capitol, the seat of Congress, it was cornered by police cruisers and armed officers on foot.

Footage aired by broadcasters showed the car executing a tight U-turn as shots rang out, and then speeding off. Shortly afterwards it hit another barrier and more shots were fired.

Lanier, while refusing to speculate on the cause of the incident, said it "does not appear in any way to be an accident. This was a lengthy pursuit."

The chief of the Capitol Police, Kim Dine, said he had no information to suggest a terrorist motive for the "isolated incident."

David Loewenberg, a 21-year-old student, said he was in his basement apartment near the Capitol when he heard "a succession of seven or eight gun shots" and rushed outside.

"I could make out a black car that had either run up on the side of the curb or crashed," he told AFP.

Loewenberg saw a police officer leaving the scene "hugging" a child in his arms. "It was a girl as far as I could tell," he said. "The child was taken away pretty quickly by the police officer."

The incident was the second major security breach in the US capital in less than three weeks. On September 16, a deranged gunman stormed the nearby Navy Yard and killed 12 people.

Thursday's scare also came three days into a US government shutdown, which has raised political tensions and caused hundreds of thousands of workers to be sent home without pay.

Senators sheltering inside the Capitol told reporters that they had heard up to six shots while police sealed off the building and emergency vehicles converged at the scene.

About half an hour after the incident began, the security lockdown at the Capitol was eased and the doors reopened.

Outside the Dirksen office building, which houses senators' offices, staff members not sent home by the shutdown could be seen taking cover behind trees and vehicles.

The White House was also briefly placed in lockdown, with Secret Service agents in tactical gear deployed around the building. The security alert was later partially lifted.

Matthew Jacobs, a 26-year-old tourist from Wellington, New Zealand, was on a bicycle near the White House when the car chase began.

He said he saw "some car try to get through a barrier. Rammed through it, bowled someone over and took off."