HAVANA (AP) — A tropical depression that quickly developed in the Caribbean headed over Cuba early Wednesday threatening to strengthen into a tropical storm as it headed toward southeastern Florida.

Cuba expected heavy rains and high winds overnight.

Early Wednesday, the storm's center was about 100 miles (160 kilometers) south of Marathon, Fla., moving north-northeast at 14 mph (22 kph), according to the U.S. National Hurricane Center in Miami.

Maximum sustained winds were 35 mph (55 kph), but the depression was forecast to strengthen some and become a tropical storm. It was expected to be near or over southeastern Florida by Wednesday evening.

Cuba's chief meteorologist, Jose Rubiera, said the weather system was large but disorganized and weak. He said the heaviest rains were expected to hit east of the storm's center in an area from Matanzas province to Las Tunas in the eastern part of the island.

Rubiera said the storm was already dumping rain on the island's southern coast Tuesday night, and predicted the rainfall would cause more problems in some mountainous regions and low-lying areas than the winds associated with the storm.

"Don't be afraid," he said during the evening newscast on state television, pointing to a model showing dark moisture associated with the storm moving over the heart of the island. "This means little in practical life."

He went on to forecast that top wind speeds would rise to no more than 50 mph (80 kph). "Those winds will not cause any damage, except possibly to sensitive crops or weak structures," he said.

An official bulletin issued by the communist government warned citizens in areas facing heavy rains to be especially vigilant, keeping a close eye on the storm's trajectory.

Cuba has a well-trained civil defense force noted for its fast response to natural disasters. The country often orders large-scale evacuations ahead of even moderate storms. But no such evacuations were immediately announced, and state media had no word on the activation of emergency plans.

While the 2010 Atlantic hurricane season has been unusually active, Tuesday's storm is the first to directly threaten Cuba. The island was devastated by three hurricanes in 2008, but was entirely spared last year.

Serious damage from a hurricane this year could be a major blow to the cash-strapped government as it attempts to right its weak economy. This month, Cuba's communist leaders announced that a half-million state employees would be laid off and reforms implemented to allow more private enterprise.

A tropical storm warning was in effect from Matanzas province eastward to Ciego de Avila in Cuba, as well as the northwestern and central Bahamas and in Florida from Sebastian Inlet to the Keys.

The depression's effects were felt Tuesday south of Cuba in the Cayman Islands, where meteorologists said more than four inches (10 centimeters) of rain fell in just 12 hours, causing flooding. Public schools closed at midday Tuesday, and government workers who live in low-lying areas were allowed to leave early.

Chief Grand Cayman Meteorologist John Tibbetts said 5- to 7-foot (1.5- to 2-meter) waves were forecast through Wednesday night and warned boaters to remain ashore.

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Associated Press Writer Tammie Chisholm in Grand Cayman, Cayman Islands, contributed to this report.