Both were forecast to become hurricanes sometime Monday.
Rafael was producing sustained winds near 60 mph with higher gusts and was expected to become a hurricane by Monday night, the National Hurricane Center in Miami said in its 5 p.m. EDT advisory.
Rafael, heading to the north-northwest at 10 mph, was centered about 185 miles north-northeast of San Juan, Puerto Rico and about 800 miles south of Bermuda, where a tropical storm watch was in effect.
The storm was generating tropical storm-force winds up to 175 miles from its center.
It was expected to stay on its current track through Sunday night, then turn to the north Monday, staying well to the east of the Bahamas, the forecasters said. It could approach Bermuda late Tuesday.
Rafael was expected to drop 4-8 inches of rain on the Leeward Islands, with isolated pockets getting 12 inches. Forecasters said the heavy rains could produced life-threatening flash floods and mud slides in mountainous areas.
The U.S. Coast Guard and U.S. Virgin Islands Department of Natural Resources were battling the conditions to search for three people who were aboard a small aircraft that crashed Saturday about 7 miles south of St. Thomas, CNN said.
The twin-engine plane took off from St. Croix and was bound for St. Thomas. One woman was rescued soon after the crash, but she said there two other men and a woman aboard the plane.
Paul also was producing 60 mph winds as it churned 625 miles southwest of the southern tip of Mexico's Baja California. The storm was heading to the northwest at 7 mph.
Because it was so far out to sea, no coastal watches or warnings were in effect related to Paul, but dangerous surf and rip tides were expected along the south and central Baja coast by Monday night.
The storm was expected to strengthen into a hurricane Monday. Paul was pushing tropical storm-force gales outward up to 80 miles from its center.
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