NORTH CHARLESTON, S.C. — 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 five deaths in South Carolina 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 over 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.