Flooding from days of relentless, saturating rains paralyzed much of South Carolina on Sunday, as vehicles were submerged, dams were pushed to their limits, electricity was cut off to thousands and emergency officials staged hundreds of swift-water rescues.

Officials attributed at least three deaths to the flooding.

The menacing weather, an agonizingly powerful blend of a low-pressure system and some of the moisture from Hurricane Joaquin as it spun through the Atlantic Ocean toward Bermuda, was expected to last into the week, raising fears that conditions could worsen.

In a response that evolved and expanded by the hour, the authorities deployed the National Guard, opened shelters, imposed curfews, closed schools and shut major thoroughfares, including more than 70 miles of Interstate 95.

“This is not going to clear up until at least Tuesday or Wednesday,” Gov. Nikki R. Haley said at a Sunday

afternoon news conference at the state’s emergency operations center near Columbia, South Carolina’s flooded capital. “Give us the space we need.”

Although other states along the Eastern Seaboard — including Delaware, Maryland, New Jersey, North Carolina and Virginia — faced weather-related troubles Sunday and had emergency declarations in effect for at least part of the day, none of their problems rivaled what unfolded here.

In the Bahamas on Sunday, the Coast Guard continued to search for El Faro, a 790-foot cargo ship missing since Thursday morning. Thirty-three people were aboard the U.S.-flagged ship when its crew said Thursday that it had partly flooded and lost propulsion as Hurricane Joaquin pounded the region and its seas.

On Sunday, the Coast Guard said search crews had found an oil sheen, containers and life preservers, but officials cautioned that the items had not been definitively linked to the El Faro.

Rescuers were locked in a similar scramble here, where by Sunday morning the floodwaters had overwhelmed some nearby neighborhoods and fishing villages. State officials were warning residents not to travel.

President Barack Obama signed a federal disaster declaration for the state on Saturday.