Tropical Storm Karen formed early Sunday, and a tropical storm warning has been issued for St. Vincent and the Grenadines, along with Grenada and its territories, the National Hurricane Center said.
Karen is about 105 miles northwest of Grenada, with maximum sustained winds of 40 mph, the center said in its latest advisory.
A tropical storm warning means that tropical storm conditions are expected somewhere within the warning area.
A tropical storm watch has been issued for the US Virgin Islands, Puerto Rico - including Vieques and Culebra - and the British Virgin Islands, according to the advisory.
Karen is forecast to continue moving in a west-northwest direction Sunday, away from the Windward Islands, and move across the eastern Caribbean Sea Sunday night and Monday.
The storm could bring enough rain to cause flash flooding and mudslides, especially in mountainous areas, on the Windward and Leeward islands, the center said.
Karen is expected to "pass near or over" Puerto Rico and the Virgin Islands on Tuesday as a tropical storm, the center said.
On the other side of the Atlantic, a low pressure system a few hundred miles southeast of the Cabo Verde Islands has a 90% chance of developing into a tropical depression or tropical storm overnight Sunday or Monday, the center said. It's heading "generally westward" over the Atlantic at about 15 to 20 mph.
Trinidad and Tobago are no longer under a tropical storm warning, the center said.