* Ernesto expected to make landfall in Mexico
* May reach hurricane strength by mid-week
* Tropical Storm Florence forms in eastern Atlantic
MIAMI, Aug 5 (Reuters) - Tropical Storm Ernesto kept on a westerly course in the Caribbean Sea on Sunday, and was expected to strengthen slowly over the next 48 hours, soaking Jamaica as it passes the island on its way to the Yucatan, U.S. forecasters said.
Officials in Jamaica issued a tropical storm warning as Ernesto moved in open waters at 22 miles per hour (35 kph) on a predicted track that should keep it at sea until a forecast landfall, possibly at hurricane strength, over Mexico's Yucatan peninsula on Wednesday.
With maximum sustained winds of 60 mph (95 kph), Ernesto was 290 miles (470 km) southeast of Kingston, Jamaica early on Sunday.
Overnight, the storm is expected to continue passing south of Hispaniola, the mountainous island Haiti shares with the Dominican Republic.
Tropical storm conditions are to strike Jamaica on Sunday afternoon as Ernesto passes south of the island. It is then expected to strengthen slowly on Monday as it moves south of the Cayman Islands, U.S. forecasters said.
Heavy rains were expected throughout Sunday in Hispaniola and Puerto Rico. Three to 6 inches (7.6 to 15.2 cm) were expected in Jamaica. Showers and thunderstorms - sometimes severe - were possible on the islands of Aruba, Curacao and Bonaire off Venezuela's northern coast.
"Ernesto is forecast to become a hurricane in the northwestern Caribbean in a day or two," the U.S. forecasters in Miami said.
The storm is not expected to strengthen significantly on Sunday, and slow strengthening is forecast for Monday. Ernesto is expected to move over the Yucatan peninsula in the next three to five days.
Ernesto, which did no reported damage on Friday as it passed over the tiny island of Saint Lucia, would be deemed a hurricane if its winds reach 74 mph (119 kph).
Forecasters expect Ernesto to move into the southern Gulf of Mexico by Thursday but it was too early to know whether it could disrupt oil and gas operations in the gulf.
U.S. National Hurricane Center forecasters said another tropical storm, called Florence, formed on Saturday in the eastern Atlantic and was moving west in open waters. As of early evening, forecasters said, Florence was about 600 miles (960 km) west of the southernmost Cape Verde Islands.
With maximum sustained winds of 60 mph (95 kph), Florence was the sixth named storm of the Atlantic-Caribbean hurricane season, moving west at 15 mph (24 kph), and was expected to near hurricane strength on Sunday.
August and September are usually the most active months of the Atlantic-Caribbean hurricane season, which runs from June 1 to Nov. 30. (Editing by Jon Hemming)