Claudette was located about 80 miles west of Columbia, South Carolina, as of 5 p.m. Sunday, according to the National Hurricane Center (NHC).
The storm has the potential for isolated tornadoes, flash flooding and gusty winds.
The tropical depression, which had maximum sustained winds of 30 mph early Sunday, is expected to restrengthen into a tropical storm by early Monday as it sweeps across North Carolina and into the western Atlantic.
Much of the North Carolina coast, from Little River Inlet to Duck, including Pamlico and Albemarle Sounds, is under a tropical storm warning, according to the NHC.
As Claudette moves off the East Coast, a storm surge of 1-3 feet is possible from the North Carolina-Virginia border south to Little River Inlet, South Carolina.
A tropical storm watch has been issued for areas of South Carolina, from South Santee River to Little River Inlet, which could see worsening conditions late Sunday or early Monday.
Parts of Alabama, Georgia and northern Florida will see heavy rain from the system throughout Sunday.
After the Gulf storm made landfall, it weakened into a tropical depression Saturday, but downpours still hammered the region.
A total of 5-15 inches of rain could fall those areas by storm’s end, the NHC said. By Saturday afternoon, some areas of Mississippi had received more than 11 inches of rain, and parts of southeastern Louisiana had received more than 8 inches, according to the weather service.
High winds also battered communities. Tropical storm-force winds — at least 39 mph — extended up to 205 miles southeast of the center of the storm early Saturday afternoon, the NHC said.
As Claudette raged as a tropical storm Saturday morning, a tornado hit the southern Alabama community of East Brewton, the Brewton Fire Department said, according to the National Weather Service.
Pictures from resident Alicia Jossey showed debris from downed trees and other materials strewn across East Brewton, a community of about 2,900 residents near the Florida state line in Escambia County.
Three people in Escambia County were injured by the tornado, according to the county’s Emergency Management Agency. The tornado also damaged several homes, and law enforcement closed US Highway 29 in East Brewton because of power lines in the roadway.
“I have peoples’ hats on my front porch and I have frames from people’s houses and little things like caulk from somebody working on something,” she said. “I have half of someone’s car seat in my backyard.”
CNN’s Haley Brink, Tyler Mauldin, Allison Chinchar, David Williams, Claudia Dominguez and Andy Rose contributed to this report.