PORT-AU-PRINCE, Haiti (AP) — Tropical Storm Isaac pushed into Cuba today after sweeping across Haiti's southern peninsula, where it brought flooding and at least three deaths, adding to the misery of a poor nation still trying to recover from the terrible 2010 earthquake.

Forecasters say the storm poses a threat to Florida Monday and Tuesday. It could eventually hit the Florida Panhandle as a Category 2 hurricane with winds of nearly 100 mph (160 kph).

The US National Hurricane Centre said a hurricane warning was in effect for Florda Keys 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. A woman and a child died in the Haitian town of Souvenance. 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.

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 they could of their possessions 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 deep, according to Rachel Brumbaugh, operation manager for the US non-profit group World Vision.

Tropical force winds extended nearly 205 miles (335 kilometres) from the storm's centre, giving Isaac a broad sweep as it passes.

Forecasters said the storm was likely to march up the Gulf of Mexico, offshore of Florida's west coast, as a hurricane on Monday.

Isaac's centre moved over Cuban soil late Saturday morning 28 miles west of Punta de Maisi, the extreme eastern tip of the island, meteorologist Jose Rubiera said on state TV.

Flooding was reported in low-lying coastal areas, and broadcast images showed powerful swells crashing onto land in the city of Baracoa. Two-hundred thirty people were in emergency shelters, according to the report.

Far to the west, the Sol Cayo Coco Hotel along the coast moved guests out of ground floor rooms, and in Havana, intermittent rains and gusty winds kept many tourists inside their hotels.

Cuba has a highly organised civil defence 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 US 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 had suspended the ferry service that connects the two sections of the base across Guantanamo Bay and many smaller craft had been 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 US military opened a detention centre on the base in January 2002.

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

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.