Tropical Storm Isaac pushed into Cuba on Saturday after sweeping across Haiti's southern peninsula, where it caused flooding and at least three deaths, adding to the misery of a poor nation still trying to recover from the terrible 2010 earthquake.

Isaac's center made landfall just before midday near the far-eastern tip of Cuba, downing trees and power lines. In the picturesque city of Baracoa, the storm surge flooded the seaside Malecon and a block inland, destroying two homes.

Forecasters said Isaac poses a threat to Florida Monday and Tuesday, just as the Republican Party gathers for its national convention in Tampa. It could eventually hit the Florida Panhandle as a Category 2 hurricane with winds of nearly 100 mph (160 kph).

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."

Scores of tents in quake settlements collapsed, including more than 50 in Cite Soleil, 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.

Doctors Without Borders said it anticipated a spike in cholera cases due to flooding and it was preparing to receive more patients.

The international airport reopened by the afternoon but there was still extensive flooding throughout Port-au-Prince after 24 hours of steady rain.

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 suspended ferry service at the Guantanamo Bay naval base and bunked guards inside prison facilities, but operations were returning to normal by late afternoon.

"The bad weather did not materialize here as tropical storm Isaac turned away," Navy Capt. Robert Durand said.

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.

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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.