Tropical storm Andrea dumped heavy rains on Florida Thursday and threatened to bring high winds and rough seas to much of the US East Coast after earlier tearing across western Cuba.

At around 2140 GMT the first named storm of the Atlantic season made landfall in Dixie County, Florida, about 10 miles (16 kilometers) south of Steinhatchee, according to the Miami-based US National Hurricane Center.

The storm -- which packed maximum sustained winds of 65 miles per hour and was moving to the northeast at 17 miles per hour -- could whip up tornadoes in central and southern Florida, the NHC said.

Forecasts take Andrea "into southeastern Georgia tonight before moving quickly up the US eastern seaboard through the weekend while gradually weakening," Florida's Emergency Operations Center said on its website.

"The primary effects from the storm are already impacting the state, with heavy rainfall expected across much of the Florida Peninsula, minor storm surge coastal flooding along the West Coast of Florida, and isolated tornadoes."

At least six possible tornadoes were reported in Florida.

Lacey Mitten told NBCMiami.com that she and her two children -- aged 11 and eight -- took cover in a bathtub as a possible tornado ripped through her neighborhood and damaged her home.

"My sister and I just looked at each other. It sounded like a freight train," Mitten said.

"We just got in the bathtub and held on."

Tropical storm warnings were in effect for a large section of Florida's west coast and reaching up north to Cape Charles Light in Virginia, the NHC said.

Minor damage and flooding was reported in coastal areas of Sarasota, south of Tampa, and Broward County to the north of Miami.

The storm was expected to dump up to eight inches (20 centimeters) of rain.

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

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

More than 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 damaged about 4,000 hectares of essential crops such as sweet potato, maize, cassava, melon and cucumber, according to the national news agency AIN.

Dried tobacco leaves were also ruined, along with seven tobacco houses.