Emergency officials said some eastern parts of the island were already being drenched by rain from Ernesto's outer bands and there was expected to be heavy rainfall and gusty winds over the island. Tropical storm conditions were expected by the afternoon from the rapidly moving storm, though U.S. forecasters said it was becoming less organized.
Jamaica's emergency management agency urged people in flood-prone areas to be on alert and avoid flooded waterways and submerged roads. The government had earlier ordered fishermen on outlying cays to evacuate and move to the main island.
Prime Minister Portia Simpson Miller called on all Jamaicans to make the necessary preparations to ensure their safety.
"I urge you to especially consider the children, the sick, persons with disabilities, the elderly, and the most vulnerable in the society," said Simpson Miller.
Daniel Edwards, a dreadlocked fisherman in Port Royal, a small fishing village at the tip of a spit of land near Kingston's airport, said vigorous lightning lit up the sky over the sea late Saturday and early Sunday.
Bailing out his small wooden fishing boat next to a dilapidated wooden dock, Edwards said he wasn't overly concerned about the tropical storm's passage.
"It's not much of a muchness," said the veteran fisherman, decked out in rain gear.
Ernesto was threatening to dump 3 to 6 inches of rain on the Caribbean island of less than 3 million people before drenching the coasts of Honduras, Belize and Mexico, possibly as a hurricane. Forecasters said it might weaken into a storm over land and then re-emerge as a hurricane in the Gulf of Mexico late next week.
A tropical storm watch was in effect for the coast of Honduras, from the border with Nicaragua westward to Punta Castilla, and the island of Grand Cayman in the Cayman Islands. Showers and thunderstorms were also still possible over the Dominican Republic and Haiti, which share the Caribbean island of Hispaniola.
The U.S. National Hurricane Center in Miami said that Ernesto was centered about 210 miles (335 kilometers) south of Kingston, Jamaica, late Sunday morning. It had maximum sustained winds near 50 mph (85 kph) and was moving swiftly westward at 23 mph (37 kph).
The storm wasn't expected to strengthen much during the day. But it was forecast to gradually begin gaining power over the next two days and possibly reach hurricane strength by Wednesday.
Many Jamaicans stocked up on bottled water, batteries and canned goods in the southern capital of Kingston.
Elsewhere, Tropical Storm Florence, which formed recently far out in the Atlantic, had stopped strengthening early Sunday, forecasters said, and was no longer expected to strengthen.
Florence had top sustained winds of 60 mph (95 kph) and is 770 miles (1,240 kilometers) west of the Cape Verde Islands. Forecasters said a gradual weakening of the storm was expected over the next couple of days.