In its 8 p.m. EDT update, the National Hurricane Center in Miami said Rafael was 85 miles east of St. Croix and about 25 miles west-southwest of St. Martin, moving northward at 12 mph, with top sustained winds of 50 mph.
Some strengthening was expected during the next 48 hours.
Tropical-storm force winds extended as far as 175 miles from the center of the storm.
Rafael was expected to follow a northward motion Saturday night, and then take a turn to the north-northwest Sunday. On its forecast track, it was likely to pass near the northern Windward Islands and the Virgin Islands Saturday night.
The storm is forecast to drop 3 to 5 inches of rain over the Lesser Antilles, the Virgin Islands, Culebra and Vieques, with as much as 10 inches possible in some areas.
Dangerous surf conditions are possible in the Lesser Antilles and the Virgin Islands through Sunday, forecasters said.
Tropical storm warnings were in effect for much of the Caribbean, including Anguilla, Barbuda, St. Kitts, Nevis, Antigua, Montserrat, Guadeloupe and many of the smaller islands.
Puerto Rico was under a tropical storm watch.
At 8 p.m., Paul was about 660 miles south-southwest of the southern tip of Baja California with maximum sustained winds of 40 mph. The storm was on a westerly course, moving ahead at 15 mph.
Paul's position far off the Mexican coast meant no coastal watches or warnings were in effect.
Forecasters said Paul, a small system with tropical storm-force gales extending just 35 miles out from its center, was expected to turn to the northwest and slow down Sunday, then veer back to a northerly course Monday.
Some strengthening was possible during the next two days.
Meanwhile, the hurricane center said as of 11 a.m. EDT Saturday, Patty was no longer a tropical cyclone. Patty's remnants were centered about 220 miles east-northeast of the central Bahamas with maximum sustained winds of 30 mph.
The storm was heading west-southwest at 5 mph and was forecast to dissipate during the evening.