Motorists were stranded during the morning rush hour, commuter trains were halted and emergency crews used boats to rescue dozens of people marooned by high water.
Many government employees were told to stay home, and tourists found that some of the major landmarks that had drawn them to Washington were closed.
"I just wanted to hear about stuff about America that I haven't heard in my history books," 10-year-old Loria Hawn of Laurinburg, N.C., said with disappointment outside the locked National Museum of American History.
CBS News' Howard Arenstein reports it was once again pouring in Washington Monday evening, and many agencies such at the IRS and Justice Department will remained closed Tuesday.
The National Archives — where the Declaration of Independence and Constitution are safe under glass — was shut down because the moat surrounding the building on Pennsylvania Avenue had flooded, spokeswoman Susan Cooper said. All records and national treasures were "safe and dry," she said.
The archives will remain closed Tuesday, just days before the Fourth of July weekend.
Flooding also closed IRS headquarters, the Commerce Department and the Justice Department, but the federal government as a whole remained in business.
The National Gallery of Art shut down because of a weather-related steam outage. The gallery uses steam to maintain the proper environment to preserve its priceless collections, a museum spokeswoman said. But the artworks were reported to be in no danger.
The National Zoo was closed to cars because of flooding in the parking lot but was open to pedestrians. Then it shut down entirely in the afternoon.
The tree that fell on the White House front lawn blocked a road, but visitors were not affected since no tours had been scheduled Monday, the National Park Service said.
More than 7 inches of rain fell in 24 hours in the city at the National Arboretum on Sunday and Monday, with up to 14 inches in parts of Delaware and 12 inches at Federalsburg, Md., on the Eastern Shore.
Just outside the city, more than 10 inches fell at Hyattsville, Md., where authorities evacuated 15 homes and used boats to rescue 69 people who were trapped inside, said Mark Brady, a Prince George's County fire and rescue spokesman. Boats also were also used to rescue 30 people marooned in Chevy Chase, Md., and some motorists had to be rescued from flooded underpasses in Washington during the night.
A mudslide piled debris as much as 5 feet deep on the Capital Beltway, which carries Interstate 95 around Washington. Motorists were urged to avoid downtown Washington and other areas because of mudslides, fallen trees and street flooding.
"The fewer people on the road, the better," Harford County, Md., spokeswoman Susan Collins said.
The Potomac River's Northwest Branch flooded U.S. 29, a major commuter route through Silver Spring, Md., with 5 feet of water and left a layer of mud that closed it for nearly a mile. "I've never seen anything like it," said Wayne A. Mowdy of the State Highway administration, who has worked in the area for 28 years.
In Elkton, Md., a 6-foot wide, 2-foot deep hole opened on I-95, blocking traffic in two northbound lanes, state police said.
Amtrak and commuter rail service also were disrupted. Metro subway service in Washington was interrupted during the morning commute by water on the electrified rails, but the trains were running again by noon.
Thousands of homes and businesses inside the city and in the Virginia and Maryland suburbs lost power.
Rain is forecast in the Washington area and other parts of the East Coast every day this week because of a low-pressure system stalled off the coast, the National Weather Service said.
"It's going to be a challenging week," said Maryland State Highway Administration spokesman David Buck.
A single-car crash that killed one person near Bowie, Md., was probably related to the weather, authorities said.