The Associated Press estimate is based on crowd photographs and comparisons with past events.
On the National Mall, the crowd stretched nearly two miles - from the Capitol to the steps of the Lincoln Memorial, where Martin Luther King Jr. delivered his I Have a Dream speech.
The bulk of the crowd was jammed into the area between the west front of the Capitol and the Washington Monument, where people stood shoulder-to-shoulder as Barack Obama was sworn in as the nation's 44th president. The crowd was so tightly packed that some people complained they felt claustrophobic.
Farther away at the Lincoln Memorial, people surrounded the Reflecting Pool.
Meanwhile, spectators were lined 10 deep in some places along the 1.5-mile inaugural parade route, which begins on Pennsylvania Avenue near the Capitol and ends in front of the White House. Most were dressed in heavy parkas and mittens. Many huddled under blanket.
Secret Service closed one entrance to the parade route in the early afternoon. At capacity, planners have said the route could accommodate 300,000 to 350,000 people.
Garth Baylor, 54, a carpenter from Washington, D.C., said no inaugural celebration could compare to this one.
"I went to Clinton's inauguration. It was nothing like this," Baylor said.
"I don't think Washington has ever had this many visitors all at once."
Crowds were so thick that medical personnel were having trouble getting to people quickly around the Mall, District of Columbia fire and EMS department spokesman Alan Etter said. Still, he said everyone who has needed help eventually received treatment.
"Obviously the crush of people downtown is making it very challenging," Etter said.
"We're doing the best we can."
For weeks, officials urged people to arrive early for the historic inauguration and throngs of revelers heeded that advice, arriving hours before daybreak.
At the Virginia Railway Express station in Fredericksburg, Va., chants of "Obama! Obama!" rang out when the line started moving at 5 am for the first train into Washington. Some had been there since before 4 a.m.
"It's so energised, it's just unexplainable. Everyone is just so happy," Cindia Velasco of Los Angeles said.
Lines of riders also formed in suburban parking lots for the Metro transit system, which added extra trains for the rush.
By noon, Metro ridership had reached more than a half-million people, transit officials said. Huge lines formed outside subway stations; many parking lots filled up and had to be closed.
Two downtown rail stations were shut down for nearly an hour starting shortly before 9:30 a.m. after a woman fell on the tracks. She was hospitalized with non-life-threatening injuries. It was not clear how the woman ended up on the tracks, spokeswoman Candace Smith said. Metro urged passengers to stand at least two feet away from the platform edge for their safety.
Police had projected crowds ranging between 1 and 2 million for the inauguration.
In 1981, President Ronald Reagan's inauguration drew about 500,000 people, and President Bill Clinton's 1993 inauguration drew about 800,000 people, according to National Park Service estimates.
Crowd counting has long been a controversial issue. The park service says Congress ordered it to stop doing crowd counts in 1997 after the agency was accused of underestimating numbers for the 1995 Million Man March.
