Alberto, with maximum sustained winds of 40 mph, was about 100 miles east-northeast of St. Augustine, Fla., and about 165 miles south of Charleston, S.C., the National Hurricane Center in Miami said in its 5 a.m. advisory.
The storm was moving on a south-southeasterly track at about 5 mph.
No coastal watches or warnings were in effect.
Alberto was expected to turn east later in the day, then shift to the northeast and pick up speed into Tuesday, the center said.
Forecasters said Alberto should remain off the Georgia and Carolina coasts on its current path.
Dangerous surf conditions, including rip currents, were possible along the coasts of northeastern Florida, Georgia and South Carolina Monday, forecasters said.
In the Pacific, the tropical depression south of Mexico was expected to strengthen to a tropical storm later Monday, the hurricane center said.
The storm, with maximum sustained winds of 35 mph, was about 520 miles south of Acapulco, Mexico, and moving west at 6 mph.
Forecasters said the depression will shift to the west-northwest with an increase in forward speed expected Monday night into Tuesday.