The first tropical storm of the 2013 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 also was issued for a swath of the East Coast, according to USA Today.

As of 8 a.m. EDT Tropical Storm Andrea, which is not forecast to strengthen into a hurricane, had winds of 60 mph and was moving to the north-northeast at 14 mph. The center of the storm was about 160 miles west of Tampa. The storm’s center should make landfall along the coast of Florida’s Big Bend this afternoon or evening, the National Hurricane Center reported.

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

A tornado watch is in effect for much of Florida.

Click play to watch a local report and forecast.

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

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

The storm 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.

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.

Click here for the full report with video.