Noel is the 14th named storm of the Atlantic season.
The strengthening Caribbean storm, which formed into a tropical storm Sunday, poses a serious threat to Haiti, where floods killed at least 37 earlier this month.
Noel had sustained winds of about 45 mph and its outer bands dumped rain over Hispaniola overnight, according to the U.S. National Hurricane Center in Miami.
At 8 a.m. EDT, Noel's center was about 80 miles east-southeast of the eastern tip of Cuba.
The meandering storm was spinning north-northwest at roughly 12 mph, on a projected track that would bring it over the southeastern Bahamas later Monday.
Forecasters said Noel, with tropical storm force winds fanning 140 miles from its center, could drop 10 to 20 inches of water on Hispaniola, southeastern Cuba and Jamaica. It's expected to turn to the northwest within 24 hours.
The combination of a building area of high pressure over the Northeast and Tropical Storm Noel were creating a very strong and persistent Northeasterly wind along the southeast U.S. coastline "and it's only going to get worse over the next few days," says CBS News meteorologist George Cullen. There will be very rough seas with dangerous rip currents from the shores of the Carolinas to the eastern beaches of Florida. It's "a bit too soon yet to know for sure if it'll remain east of Florida."
Dominican authorities said at least 600 people had been evacuated as the storm touched off landslides, flooded rivers and pushed storm surges onto Santo Domingo's seaside boulevard.
Swollen rivers also forced evacuations in Cabaret, a town north of Port-au-Prince where floods killed at least 23 people earlier this month, said Marie Alta Jean-Baptiste, director of Haiti's civil protection agency.
"We are working hard to make sure everything goes well and that every citizen knows a cyclone is coming," Jean-Baptiste said. It could take days for Haitian authorities to learn of flooding in some parts of the country, where communications are limited.
Flood concerns on Saturday forced three U.S. senators to cut short a trip to Haiti, where they'd planned to survey damage caused by earlier storms.
"It was just raining like mad," Sen. Tom Harkin, D-Iowa, told The Associated Press before flying out of Port-au-Prince Saturday evening. Sens. Jeff Bingaman, D-N.M., Bob Corker, R-Tenn., were also visiting.
Widespread deforestation and poor drainage mean that even moderate rains can cause devastation in Haiti, where thousands of people build ramshackle homes in flood plains.
In 2004 the Caribbean nation was hit by Tropical Storm Jeanne, which triggered flooding and mudslides that killed more than 2,000 people. That storm later strengthened into a hurricane.