PORT-AU-PRINCE, Haiti — Tropical Storm Isaac swept across Haiti's southern peninsula early Saturday, bringing flooding and at least three deaths while adding to the misery of a poor nation still trying to recover from the terrible 2010 earthquake.

The storm was heading toward eastern Cuba and forecasters said it poses a threat to Florida by Monday and Tuesday, just as the Republican Party gathers for its national convention in Tampa. The U.S. National Hurricane Center in Miami said a hurricane warning is in effect for the Florida Keys and for the west coast of Florida from Bonita Beach south to Florida Bay.

At least three people were reported dead. 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.

In the shantytown of Cite Soleil, just north of Port-au-Prince, about 300 homes had either their roofs blown off or sitting in three feet of water, according to Rachel Brumbaugh, operation manager for the U.S. nonprofit group World Vision.

"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.

Forecasters said Isaac could dump as much as eight to 12 inches and even up to 20 inches on Hispaniola, which is shared by Haiti and the Dominican Republic, as well as produce a storm surge of up to 3 feet.

Isaac was centered about 95 miles east-southeast of Guantanamo Bay, Cuba, early Saturday, with maximum sustained winds of 60 mph. It was moving northwest at 14 mph. Tropical force winds extended nearly 200 miles from the storm's center.

Forecasters said the storm was likely to march up the Gulf of Mexico, off Florida's west coast, as a hurricane on Monday, just as the Republican National Convention is scheduled to start. Tampa was within the storm's possible strike zone, but the most likely course would carry it toward landfall on the Florida Panhandle late Tuesday or early Wednesday.

Cuba declared a state of alert Friday for six eastern provinces and five central provinces were put on preliminary watch. Vacationers in tourist installations of those regions were evacuated.

State television began an all-day transmission of news about the storm on Saturday.

Radio Baracoa, from the city of Baracoa on the northern coast of eastern Cuba, reported that high seas began topping the city's seawall Friday night. Reports said lower than normal rains had left reservoirs well below capacity and in good shape to absorb runoff.

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.

In Port-au-Prince, a city of some 3 million ringed by mountains, authorities and aid workers tried to evacuate people from a tent camp to temporary shelters.

More than a hundred people were at a shelter in a school that President Michel Martelly toured Friday, but after the visit some people began to leave.

"They dragged me from the camp and brought me here," 38-year-old Marlene Charles, thirsty and hungry, said about the aid groups. "There's no way I'm going to spend the night here."

In the Dominican Republic, authorities said they evacuated nearly 3,000 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 out in parts of the capital, Santo Domingo, but there were no reports of injuries.

Organizers of next week's Republican National Convention in Tampa were monitoring storm developments, and authorities said there were no plans to cancel the convention.

Out in the eastern Atlantic, former Tropical Storm Joyce degenerated into a weak low pressure system Friday.