COLUMBIA, S.C. (AP) — A dangerous rainstorm drenching the East Coast brought more misery Sunday to South Carolina — cutting power to thousands, forcing dozens of water rescues around the capital city and closing "too many roads to name" because of floodwaters.

Early Sunday, emergency management officials sent a statewide alert telling people to stay off roads and remain indoors unless their homes were in danger of flooding. Interstates were closed by flooding in several spots, and nearly 30,000 customers were without power.

The region around the state capital of Columbia was being hit particularly hard, with the city's police department tweeting: "Too many roads to name that are flooded. Please heed our warning! DO NOT venture out!"

The city's fire department had already made more than 50 swift-water rescues by the early morning and was responding to dozens more calls. Local news showed images of rescuers wading into waist-deep water to help drivers trapped at a busy intersection.

The Columbia area received the most rain in the state overnight, with up to 14 inches reported in some places since Saturday, forecasters said. To the southeast, meanwhile, rainfall had exceeded two feet since Friday in some areas around Charleston, though conditions had improved enough that residents and business owners were allowed back into the waterlogged downtown on a limited basis.

The South Carolina Highway Patrol responded to more than 300 collisions around the state in the 12 hours leading up to 6 a.m. It cleared nearly 140 trees from roads.

President Barack Obama declared a state of emergency in South Carolina and ordered federal aid to bolster state and local efforts.

At least five weather-related deaths have been reported since rains began spreading over the Eastern Seaboard, which appeared to dodge the full fury of Hurricane Joaquin that's veering out to sea.

The steady downpour around the Southeast has drawn tropical moisture from offshore that's linked up with an area of low pressure and a slow-moving front. Heavy rain was expected to continue in the Carolinas and parts of northern Georgia and could cause some significant river and stream flooding, the National Weather Service said.

The low-pressure system also was expected to whip up stiff northeasterly winds in the Blue Ridge mountains of the Carolinas and western Virginia with gusts up to 35 mph through Sunday, the weather service said. Increased winds held the prospect of toppling trees in waterlogged soil.

High winds toppled a tree that hit a vehicle and killed a passenger Thursday near Fayetteville, North Carolina. Three people died in separate weather-related traffic accidents in South Carolina on Friday and Saturday, the Highway Patrol said. A drowning in Spartanburg, South Carolina, also was linked to the storm.

The downtown Charleston peninsula, which includes the city's historic district, has been reopened on a limited basis. City officials closed the area to incoming traffic Saturday because of flooding from heavy rains.

Residents and business owners are again being allowed in along with public safety workers and medical workers. More than 60 streets and intersections remain closed because of high water.

Flooded roads were closed throughout the mid-Atlantic region and power companies reported scattered outages in several states.

In the Greenville area 100 miles northwest of Columbia, some were venturing out for necessities despite the warnings.

"It's wet, but nothing we can't handle," said Michael Robertson, 54, who was grabbing a pack of cigarettes at a gas station on Sunday.

He said he stayed inside Saturday, but he said he was going "a little stir crazy."

"I had to leave the house," he said. "When I got up, I didn't know what to expect. I saw flooding all over the state, but after driving around a little bit, I think we dodged a bullet here."

___

Contributing to this report were Associated Press writers Bruce Smith in Charleston, South Carolina; Mitch Weiss in Greenville, S.C.; Brock Vergakis in Norfolk, Virginia; David Dishneau in Ocean City, Maryland; Bruce Shipkowski in Trenton, New Jersey, and Julie Walker in New York.