Hurricane watches were posted for Barbados, Grenada, St. Lucia and St. Vincent and the Grenadines, meaning hurricane-force wind could be felt there late Wednesday or early Thursday, the National Hurricane Center said. A tropical storm watch was issued for Tobago.
The storm is forecast to be near Puerto Rico by Friday and could approach the U.S. mainland early next week.
At 2 p.m. EDT, Emily was centered 530 miles east-southeast of Barbados and was moving west at about 20 mph, up from 13 mph on Monday. It had maximum sustained wind of about 50 mph and was expected to strengthen while gradually turning toward the west-northwest.
Hurricanes have sustained wind of at least 74 mph.
Emily grew into a tropical storm late Monday, the earliest date on record that five named storms had developed, the hurricane center said.
Meanwhile, it's another day of assessing damage and cleaning up the debris left behind by the fourth named storm, Hurricane Dennis. Thousands of residents ventured out to survey the damage, and most of them, reports CBS News Correspondent Trish Regan, were relieved.
The heaviest damage was in the Florida communities of Gulf Breeze, Pensacola Beach and Navarre Beach, which were all slammed by Ivan.
Jason Wilburn of Navarro Beach didn't know what to expect when he ventured back to his seaside home.
"A little nervous," he said as he went home. And then: "That's my house and I'm so glad it's still here."
Alabama Power says only 37,000 of its customers are still without power, down from a peak of nearly 240,000.
In the northwestern Florida panhandle town of Century, Marion Cooper's general store was being powered by a generator. The entire town, which was hard hit by the storm, is without electricity, reports CBS News Correspondent Cami McCormick; nearly every home suffered some sort of damage. Still, Cooper says the town was lucky.
"Oh, yeah, we're alive!" he laughed.
Remnants of Hurricane Dennis could bring more than rainfall to the Midwest's parched fields: The storm clouds also could carry spores of a potentially devastating soybean fungus.
When Dennis made landfall along the Gulf Coast Sunday, its winds swept an area of southwestern Alabama where fields are infected with soybean rust, said Purdue University plant pathologist Greg Shaner. The storm then moved inland toward the Tennessee and Ohio river valleys.