At least three people died in Haiti as Tropical Storm Isaac triggered mudslides and flooding there before heading back over water and towards Cuba. Isaac should become a Category 1 hurricane on Sunday just as it nears the Florida Keys, the U.S. National Hurricane Center said, and then grow into an even stronger Category 2 storm.

"Hurricane conditions are expected in the hurricane warning area in southwest Florida and the Florida Keys on Sunday," the center said in a Saturday morning advisory.

The center now expects Isaac to build to a Category 2 hurricane, with winds up to 110 mph, after it enters the warmer waters of the Gulf of Mexico.

In Haiti, a woman and a child in the town of Souvenance were killed in the storm, a local official reported.

In the capital Port-au-Prince -- where some 350,000 people are still living in tents or shelters after the 2010 Haiti earthquake -- a girl, 10, was killed when a wall fell on her.

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© Dieu Nalio Chery/APResidents wade through a flooded street in Port-au-Prince, Haiti, on Saturday.
Power outages and flooding were reported as Isaac moved across the hilly and severely deforested Caribbean country.

"There's a lot of rain, a lot of wind," said Magdala Jean-Baptiste, who huddled with her frightened children in their home in the southern coastal city of Jacmel. "We haven't had any power since the storm started yesterday. We passed the night with no sleep."

Cuba prepared by closing beaches and evacuating tourists in vulnerable areas, NBC's Mary Murray and The Weather Channel's Mike Seidel reported from Havana. Flights across Cuba were also suspended.

In Baracoa, a city on Cuba's eastern side, high seas began topping the seawall Friday night, Radio Baracoa reported.

Now with 60 mph winds, Isaac should exit Cuba on Sunday and then move south of the Florida Keys and into the Gulf.

Republicans are preparing to gather in Tampa, on Florida's central Gulf Coast, for Monday's start of their national convention ahead of the November presidential election.

The convention is expected to proceed as planned but Gulf of Mexico operators began shutting down offshore oil and gas rigs on Friday ahead of the storm.

Tampa's weather forecast includes rain and high winds Sunday night and into Monday, The Weather Channel reported. The winds could gust up to 60 mph.

Monday and Tuesday include a risk of tornadoes across south Florida.

Isaac's exact path is still unclear, but the hurricane center said models suggest it will make landfall somewhere between the Florida Panhandle and New Orleans on Tuesday night.

The storm's anticipated path did shift closer to the Keys than previously forecast and emergency managers urged tourists to leave the islands if they could do so safely. A single road links the chain of islands to the Florida Peninsula.

Reuters and The Associated Press contributed to this report.