Tropical Storm Ernesto brushed past the Caribbean country's southern coast Sunday, causing heavy rains but few problems as it took a course expected to carry it by Honduras and across the Yucatan Peninsula into the Gulf of Mexico.

Forecasters at Jamaica's Meteorological Service said rain had tapered off by Sunday evening although light to moderate showers from squalls were still reported across most of the island, especially eastern areas.

In Jamaica's southern capital of Kingston, Ernesto dumped some rain but left no noticeable damage.

Island authorities urged people in flood-prone areas to stay on alert and urged fishermen on outlying cays and banks to remain in safe harbors on the main island.

As the storm's outer bands approached earlier, 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," she said.

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 by the storm.

"It's not much of a muchness," said the veteran fisherman, decked out in rain gear.

Forecasters said Ernesto could begin drenching the coast of Honduras on Monday. It is then expected to strengthen, possibly becoming a weak hurricane, before moving ashore near the Belize-Mexico border Tuesday night and passing into the Gulf of Mexico.

The U.S. National Hurricane Center in Miami said Ernesto had become a bit more organized as it moved away from Jamaica and its forward movement had slowed some.

A tropical storm watch was in effect for the coast of Honduras, from the border with Nicaragua westward to Punta Castilla, and the main island of Grand Cayman in the Cayman Islands.

A Cayman government statement urged Grand Cayman residents to monitor the storm but said the storm was not likely to have serious effects on the British Caribbean territory.

The U.S. hurricane center said Ernesto was centered about 235 miles (375 kilometers) east of Cabo Gracias a Dios on the Nicaragua-Honduras border late Sunday. It had maximum sustained winds near 50 mph (85 kph) and was moving westward at 15 mph (24 kph).

Elsewhere, Tropical Storm Florence, which formed far out in the Atlantic, stopped strengthening by early Sunday and was no longer expected to gain strength, the hurricane center said.

Florence's top sustained winds had slowed further to 40 mph (65 kph) by late Sunday and it was 925 miles (1,485 kilometers) west of the Cape Verde Islands. Forecasters said a gradual weakening was expected and the storm was likely to become just a tropical depression on Monday.

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David McFadden on Twitter: http://twitter.com/dmcfadd