The National Hurricane Center in Miami said in its 8 p.m. EDT advisory the storm -- upgraded earlier Tuesday from a tropical depression -- was about 435 miles east of Guadeloupe with top sustained winds of 40 mph, and was moving west at 17 mph and whipping tropical storm-force gales outward up to 45 miles.
The hurricane center said a tropical storm warning was in effect for Martinique, Dominica, Guadeloupe and the surrounding islands, St. Martin, St. Kitts, Nevis, Antigua, Montserrat, Anguilla, Barbuda, St. Eustatius and St. Maarten.
A tropical storm watch was issued for the British Virgin Islands, Puerto Rico, Vieques, Culebra and the U.S. Virgin Islands.
The forecasters said people in Hispaniola and Cuba should monitor the storm's progress.
Forecasters said Isaac was expected to stay the course and strengthen during the next couple of days, moving through the central Lesser Antilles Wednesday evening and emerging over the eastern Caribbean Sea Thursday morning.
Isaac is capable of producing 4-8 inches of rain over the northern Windward Islands and the Leeward Islands, with 1-3 inches expected over Puerto Rico and the Virgin Islands.
Storm surges of 1-3 feet above normal tide levels are forecast for the northern Leeward Islands, with dangerous waves there and in the Windward Islands.