HAVANA — 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 on 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 miles per hour.
Florida Governor Rick Scott declared a state of emergency, officials urged vacationers to leave the Florida Keys, and the 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, Senator 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 3 feet deep, according to Rachel Brumbaugh, operation manager for the US nonprofit group World Vision.
Isaac was centered about 40 miles north of Guantanamo Bay, Cuba, with maximum sustained winds of 60 miles per hour, the Hurricane Center reported. It was moving northwest at 17 miles per hour.
Tropical storm-force winds extended nearly 205 miles from the center, giving Isaac a broad sweep as it passed.
Forecasters said the storm was likely to march up the Gulf of Mexico, off of Florida’s west coast, as a hurricane Monday, just as the Republican 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.
Scott, the governor of Florida, said 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.
Isaac’s center 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.
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.
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 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 damage to crops.