Tropical storm Andrea churned toward Florida Thursday with the threat of heavy rains and tornadoes, after damaging crops in Cuba and forcing the evacuation of some 2,600 people.

As of midday the first named storm of the Atlantic season packed maximum winds of 95 km per hour (60 mph) as it moved northeast at 22 kilometers per hour (14 mph).

It was 255 kilometers (160 miles) west of Tampa and expected to pick up speed over the course of the day, the National Hurricane Center in Miami said, adding that Andrea carried the potential for whipping up tornadoes in central and southern Florida.

The National Oceanic and Atmospheric Administration has said this hurricane season -- it runs from June 1 to November 30 -- will be particularly busy, with up to 20 tropical storms and as many as 11 hurricanes -- and up to six of them intense.

In Cuba, rain fell for seventh straight day Thursday as Andrea moved away from the island's western tip after forcing the evacuation of 2,600 people.

Some 30 villages were cut off by water, and in one hamlet more than 200 houses were submerged, the official newspaper Granma said

The storm also caused crop damage that is still being tallied, it added.