The US National Hurricane Center in Miami said that Ernesto was centered about 215 miles (345 kilometers) southeast of Kingston, Jamaica, around dawn Sunday. It had maximum sustained winds of about 50 mph (85 kph) and was moving westward at 22 mph (35 kph).
The storm wasn't expected to strengthen much during the day. But it was forecast to gradually begin gaining power Monday in the warm Caribbean waters and possibly reach hurricane strength by Monday evening.
With forecasters predicting possible rains of up to three to six inches in Jamaica, islanders stood in long lines at grocery stores in the island's capital of Kingston to buy bottled water, bread and canned goods.
"We're going to have heavy rains, so I'm stocking up," said Marco Brown, a Kingston resident in his late 50s.
The Jamaican government ordered fishermen on outlying cays to evacuate and move to the main island.
The hurricane center said Jamaicans should brace for tropical storm conditions beginning Sunday afternoon. Occasionally heavy showers and thunderstorms also were possible over the Dominican Republic and Haiti, it said.
Elsewhere, Tropical Storm Florence, which formed recently far out in the Atlantic, had stopped strengthening early Sunday, forecasters said.
Florence had top sustained winds of 60 mph (95 kph) and is 680 miles (1,090 kilometers) west of the Cape Verde Islands. But the forecasters said the storm was expected to begin strengthening anew in the next day or so.