The woman who drove the black Infiniti involved in the chase died from gunfire, police said, and a year-old child in the car with the woman was in protective custody.
Two law enforcement officers were injured -- a Secret Service officer hit by the car near the White House, and a Capitol Police officer whose vehicle crashed during the chase, authorities said.
The dramatic events brought a swarm of emergency vehicles to the Capitol complex and caused Congress and surrounding offices to be temporarily locked down.
House and Senate sessions were immediately suspended, with legislators ordered to take cover and keep away from windows. Police also closed Pennsylvania Avenue in front of the White House.
The chase began when the Infiniti hit a barrier on the outer security perimeter of the White House, said Ed Donovan, a Secret Service spokesman. One of the responding officers was hit by the car as it left the scene, he said.
Police said the car sped down Pennsylvania Avenue toward the Capitol, where security vehicles stopped it at Garfield Circle.
Frank Schwing, a Washington resident who was near the area, said officers "came out with their guns drawn" and approached the suspect's vehicle.
"At that point, the driver slammed into reverse, slammed into a cruiser, did a 180 (degree turn), took off, and at that point, there were a half dozen or so shots fired," apparently all by small arms from police, Schwing told CNN.
Video footage by other witnesses showed the black vehicle then careening around a nearby traffic circle with a police car in close pursuit and then headed away. Shortly afterward, the black car crashed into security barriers a few blocks, witnesses said.
Cathy Lanier, the chief of the Metropolitan Police Department, said more shots were fired after the vehicle stopped, and the woman was hit several times. She was later pronounced dead, Lanier said.
According to multiple sources, there was no reason so far to believe that the woman fired any shots or even had a weapon.
A task force prepared to execute a search warrant at her Connecticut home, law enforcement sources said.
In Congress, a Capitol Police bulletin said reports of gunshots required "all occupants in all House office buildings to shelter in place."
"Close, lock and stay away from external doors and windows," the bulletin said. Authorities later lifted the lockdown, with police saying they believed the incident was isolated with no connection to terrorism.
President Barack Obama was briefed on the situation, which occurred on the third day of a government shutdown due to a stalemate in Congress over government funding.
"The timing on this was really kind of scary," said Republican Rep. Blake Farenthold of Texas. "Capitol Hill police are at a lower personnel level because of the shutdown."