The first tropical storm of the Atlantic hurricane season got a little stronger early Thursday as it headed toward Florida's western coast and a new tropical storm warning was issued for a swath of the U.S. East Coast.

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, Florida, all the way to Cape Charles Light in Virginia.

Tropical Storm Andrea's maximum sustained winds increased to near 95 km/h, and the storm was expected to make landfall in Florida's Big Bend area Thursday afternoon before moving across southeastern Georgia and the Carolinas. It was not expected to strengthen into a hurricane.

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

Storm surge would be the biggest threat as the storm comes onshore, Blake said. He added that flash flooding was also a concern, with up to 15 centimetres of rain expected. Isolated areas in Florida and southeastern Georgia could get 20 centimetres of rain.

Tornado warning may be issued

Already, the National Weather Service in Tampa confirmed two tornados touched down early Thursday — one in Myakka City and the other in Sun City Center. There were no reports of injuries.

Tornado warnings and watches could be issued throughout the day.

The storm was expected to hug the coastline, bringing rain as far as the southern New England area through the weekend.

As of about 5 a.m. ET Thursday, the storm was centered about 355 kilometres west-southwest of Tampa and was moving north-northeast near 20 km/h.

In Florida, Gulf Islands National Seashore closed its campgrounds and the road that runs through the popular beach-front park Wednesday. The national seashore abuts Pensacola Beach and the park road frequently floods during heavy rains. On Pensacola Beach, condominium associations asked people to remove furniture on high balconies because of the expected high winds and beach lifeguards warned tourists of possible high surf.