Florida Gov. Rick Scott declared a state of emergency, officials urged vacationers to leave the Florida Keys and the U.S. National Hurricane Center said a hurricane warning was in effect there, as well as for the west coast of Florida from Bonita Beach south to Ocean Reef and for Florida Bay.
At least three people were reported dead in Haiti. A woman and a child died in the town of Souvenance, Sen. Francisco Delacruz told a local radio station. A 10-year-old girl died in Thomazeau when a wall fell on her, said Marie Alta Jean-Baptiste, director of Haiti's Civil Protection Office. She said as many as 5,000 people were evacuated because of flooding.
Many, however, stayed and suffered.
The Grive River overflowed north of Port-au-Prince, sending chocolate-brown water spilling through the sprawling shantytown of Cite Soleil, where many people grabbed what possessions they could and carried them on their heads, wading through waist-deep water.
"From last night, we're in misery," said Cite Soleil resident Jean-Gymar Joseph. "All our children are sleeping in the mud, in the rain."
More than 50 tents in a quake settlement collapsed, forcing people to scramble through the mud to try to save their belongings.
About 300 homes in Cite Soleil lost their roofs or were flooded three feet (one meter) deep, according to Rachel Brumbaugh, operation manager for the U.S. nonprofit group World Vision.
Isaac was centered about 40 miles (65 kilometers) north of Guantanamo Bay, Cuba, with maximum sustained winds of 60 mph (95 kph), the Hurricane Center reported. It was moving northwest at 17 mph (28 kph).
Tropical storm-force winds extended nearly 205 miles (335 kilometers) from the center, giving Isaac a broad sweep as it passed.
Forecasters said the storm was likely to march up the Gulf of Mexico, offshore of Florida's west coast, as a hurricane on Monday, just as the Republican National Convention is scheduled to start.
Tampa is within the tropical storm watch zone, meaning forecasters believe tropical storm conditions are possible there within the next 48 hours.
Gov. Scott said during a media briefing that delegates were being told how to stay safe during a storm, and officials were ready for storm surge, bridge closures and other problems that could arise during the convention.
Isaac's center moved over Cuban soil late Saturday morning 28 miles (45 kilometers) west of Punta de Maisi, the extreme eastern tip of the island, meteorologist Jose Rubiera said on state television.
In Baracoa, authorities cut off electricity as a preventive measure. Civil defense officials patrolled the streets and told onlookers to be careful as they gawked at the powerful surf kicked up by the storm. Waves crashing against the seawall sent spray high into the air and deposited rocks and other debris on land.
Dariel Villares and a cousin who lives next door lost their seaside homes.
"A high wave came and knocked down both walls, mine and my cousin's," Villares said. "Now we're removing everything of value."
There were no reports of fatalities, Red Cross worker Javier de la Cruz said.
Flooding was reported in low-lying coastal areas and 230 people were in emergency shelters, according to state TV.
Far to the west, the Sol Cayo Coco beach resort moved guests out of ground floor rooms. Intermittent rains and gusty winds buffeted Havana, 560 miles (900 kilometers) away.
Cuba has a highly organized civil defense system that goes door-to-door to enforce evacuations of at-risk areas, largely averting casualties from storms even when they cause major flooding and significant damage to crops.
Near the island's southeastern tip, the U.S. military was expecting winds of up to 40 mph (65 mph) at the Guantanamo Bay naval base, said Navy Capt. Robert Durand, a spokesman for the prison there.
Ahead of the storm, roads were closed to all but emergency vehicles, the Navy suspended the ferry service that connects the two sections of the base across Guantanamo Bay and many smaller craft were pulled from the water, Durand said. All 168 prisoners were in buildings capable of withstanding storm-force winds and the guards were bunking inside prison facilities instead of returning to their quarters for the night.
One hurricane and three tropical storms have hit the base since the U.S. military opened a detention center there in January 2002. The most recent was Hurricane Thomas in November 2010, when the Navy recorded winds of 60 mph.
Authorities in the Dominican Republic evacuated nearly 7,800 people from low-lying areas, and at least 10 rural settlements were cut off by flooding, according to Juan Manuel Mendez, director of rescue teams. Power was knocked out in parts of the capital, Santo Domingo.
There were no reports of injuries, but 49 homes across the country were destroyed.
Rainfall was expected to reach up to 12 inches (300 millimeters) over the weekend.
"We still have a big cloudy area over the island that will produce lots of rain" until Sunday afternoon, said Francisco Holguin of the local meteorological agency.
Associated Press journalists Trenton Daniel and Evens Sanon in Port-au-Prince, Haiti; Anne-Marie Garcia in Havana; Fernando Gonzalez in Baracoa, Cuba; and Ezequiel Abiu Lopez in Santo Domingo, Dominican Republic, contributed to this report.