(CNN) -- Tropical Storm Alberto, meandering off the coast of South Carolina, was expected to stay offshore, and forecasters Sunday canceled a tropical storm watch for coastal areas.

As of Sunday afternoon, the center of Alberto was about 105 miles southeast of Savannah, Georgia, and about 130 miles south of Charleston, South Carolina, the National Hurricane Center said.

Packing 45-mph winds, the storm was moving southwest at near 6 mph, but was expected to slow down and drift southward Sunday night before accelerating Monday and Tuesday and moving northeast -- away from the coast.

"On this track, the center of Alberto is expected to stay off the Georgia and Carolina coasts," forecasters said.

Alberto, the first named tropical storm of the 2012 Atlantic hurricane season, formed Saturday in the Atlantic. A storm watch had been issued for an area between the Savannah River -- the border between Georgia and South Carolina -- northward to South Santee River, South Carolina.

Dangerous surf conditions, including rip currents, remained possible along the coasts of northeastern Florida, Georgia and South Carolina through Monday, the hurricane center said.

Tropical storm-force winds extended up to 60 miles from Alberto's center.

The National Weather Service in Charleston said Alberto's strongest winds would remain offshore, but some associated rain showers would affect the coast, although heavy rainfall was not expected. Shallow coastal flooding was also possible during high tide, forecasters said.

Despite being over the warm waters of the Gulf Stream, Alberto is not expected to intensify much over the next couple of days. That is due, in part, to the presence of a cool and dry air mass to the north and west of the tropical storm, CNN meteorologist Sean Morris said.

This year marks the first time in recorded history that a tropical storm has formed in both the east Pacific basin and Atlantic basin before the official start of hurricane season, the hurricane center said. The Pacific storm was called Aletta.

The Atlantic hurricane season officially begins on June 1.