The first tropical storm of the Atlantic hurricane season got a little stronger early Thursday as it headed toward Florida’s western coast, bringing drenching rain to much of the state. A new tropical storm warning was also issued for a swath of the U.S. East Coast.

As of 8 a.m. ET, Tropical Storm Andrea had winds of 60 mph and was moving to the north-northeast at 14 mph. The center of the storm was located about 160 miles west of Tampa.

"The rain covers a good portion of the Florida peninsula even though the center is a couple of hundred miles offshore," said Eric Blake, a hurricane specialist at the National Hurricane Center in Miami..

Tropical storm warnings were in effect for a large section of Florida’s west coast from Boca Grande to Indian Pass and for the East Coast from Flagler Beach, Fla., all the way to Cape Charles Light in Virginia.

Andrea will bring heavy rain, gusty winds, rough surf and severe thunderstorms to much of Florida on Thursday, according to AccuWeather meteorologist Alex Sosnowski.

As much as 4-7 inches of rain is possible from Andrea across much of northern Florida over the next couple of days, the weather service reports. Flood watches have been posted for much of Florida, Georgia and the Carolinas.

The storm’s center should make landfall along the coast of Florida’s Big Bend on Thursday afternoon or evening, the hurricane center reports.

Tropical Storm Andrea is forecast to make landfall in Florida late Thursday and then head up the Eastern Seaboard on Friday and Saturday.(Photo: Janet Loehrke, USA TODAY)

It is then forecast to head up the Eastern Seaboard on Friday and Saturday, delivering heavy rain and thunderstorms from the Mid-Atlantic to New England.

Andrea is not forecast to strengthen into a hurricane.

The system has already produced drenching rain in Mexico’s Yucatan Peninsula and in western Cuba, the hurricane center reported. Influences from Andrea have contributed to the 13.9 inches of rain that Bahia Honda, Cuba, has received since Monday, AccuWeather reports.

The National Weather Service in Tampa also confirmed two tornadoes touched down early Thursday — one in Myakka City and the other in Sun City Center. Meteorologist Rodney Wynn said there were reports of downed tree limbs and power lines and minor damage to the porch on at least one home. There were no reports of injuries.

A tornado watch was in effect for much of the state of Florida.