Tropical storm Ernesto swept by Jamaica and churned toward the Central American coast Sunday as US forecasters predicted it would gain strength in the coming days.

At 0000 GMT, the eye of the storm was located about 395 kilometers (245 miles) east of Cabo Gracias a Dios on the border between Nicaragua and Honduras, according to the Miami-based National Hurricane Center.

With top winds of 85 kilometers per hour (50 miles per hour), Ernesto was moving westward at 32 kilometers per hour (20 miles per hour).

Jamaica, under a tropical storm warning, buckled down as Ernesto passed south of the island, where it was expected to dump up to 10 centimeters (4 inches) of rain.

"Tropical storm conditions are expected in Jamaica through this evening," the NHC said.

Later Sunday and early Monday, Ernesto's eye was expected to pass south of the Cayman Islands -- where a tropical storm watch was in effect for Grand Cayman.

Parts of the Honduran coast west of the Nicaraguan border were also under a tropical storm watch.

In anticipation of fierce weather heading its way, the Nicaraguan government ordered "the evacuation of hundreds of families" from the area where the storm is likely to have some impact Monday morning, said spokeswoman and first lady Rosario Murillo.

Estimates of the number of people to be evacuated range anywhere between 600 to 1,500 people, according to official sources.

In the Dominican Republic, meanwhile, authorities were on the alert for flash floods and landslides. Late Saturday, heavy downpours had caused some flooding in the capital Santo Domingo.

A forecast model showed that the storm was not expected to become a hurricane until Friday but some strengthening was expected as it moves over the western Caribbean Sea Monday and Tuesday, the NHC said.

"Belize and the Yucatan Peninsula of Mexico should monitor the progress of Ernesto," it warned.

The current forecast model has the storm brushing the northern coast of Honduras starting at the country's border with Nicaragua.

The storm is also expected to hit Belize and parts of Guatemala before passing over the Mexican state of Quintana Roo, home to the busy beach resort city of Cancun, on Wednesday, according to the model.

Further east, Tropical Storm Florence -- the sixth named storm of the Atlantic season -- had top winds of 31 kilometers per hour (50 miles per hour) as it headed westward at 22 kilometers per hour (14 miles per hour).