(CNN) -

Tropical Storm Ernesto churned south of Jamaica on Sunday, becoming a bit more organized as it continued its westward march.

As of Sunday night, the storm was about 245 miles (395 kilometers) east of Cabo Gracias a Dios on the Nicaraguan-Honduran border, the National Hurricane Center reported. Ernesto was moving west at 20 miles per hour with maximum sustained winds of about 50 mph.

A tropical storm warning was in effect for Jamaica, where up to 4 inches of rain were predicted.

On the forecast track, the storm is expected to pass to the south of the Cayman Islands and move north of the northeastern coast of Honduras late Monday and Monday night.

Some strengthening is forecast as Ernesto moves over the Caribbean Sea.

Meanwhile, Tropical Storm Florence continued to weaken.

No coastal watches or warnings were in effect for the storm, which was some 925 miles (1,485 kilometers) west of the Cape Verde Islands on Sunday night, the hurricane center said.

It was moving west at about 13 miles per hour.

Maximum sustained winds dipped to 40 mph, and further weakening is forecast in the coming days. Florence is expected to become a tropical depression on Monday.