Tropical storm Alberto has drenched Cuba, with some parts of the island receiving as much as 50 centimetres of rainfall.
It is expected to turn towards the US state of Florida in the next few days, however is not expected to intensify into a hurricane.
US officials said the first tropical storm of 2006 carried "life threatening" rains.
"Alberto is expected to produce total rainfall accumulations of 25 to 50 centimetres over the western half of Cuba with isolated totals of 30 inches (75 centimetres) over the higher terrain," the US National Hurricane Centre said.
"These rains could produce life-threatening flash floods and mud slides," said the Miami forecasters.
State television showed pictures of extensive flooding, with one resident of Juventud island saying he had not seen such high water levels in 30 years.
Last year's record-breaking hurricane season saw the region lashed by 28 storms, 15 of which went on to become hurricanes.
The US centre issued a tropical storm watch for the western coast of Florida, meaning that storm conditions are possible from north of Bonita Beach to Steinhatchee within 36 hours.
Alberto formed off Cuba's western coast, and authorities said it is moving north at 15 kilometres an hour.
"What is unusual about the storm is not its strength, but is width, the centre said.
"The strongest winds in this tropical storm are well removed from the centre and extend mainly eastward up to 370 kilometres" said the Miami-based weather service.
Cuban Civil Defence officials evacuated 25,000 persons from low-lying areas in Pinar del Rio in western Cuba.
The Isle of Youth, south of Havana, was cut off from air and sea transportation because of heavy rains, local television news reported.
Alberto is the first tropical depression to gain tropical storm strength, and so the first to earn a name.
Tropical storms must have sustained winds of 63 kph and less than 118 kph, after which they become a hurricane.
Two thousand students in Cuba were sent home from schools on Saturday, the official National Information Agency said.
In the past two weeks, torrential rains killed seven people in Havana and two others in the eastern part of the country.