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Miami, Florida (CNN) -- Hurricane Paula inched closer to Cuba Wednesday night, a weakened storm with a slowing forward speed, forecasters said.
Paula is expected to cross on or near the Cuba's western tip late Wednesday or early Thursday.
As of 8 p.m. ET, the center of Paula, downgraded to Category 1 storm, was about 40 miles (65 kilometers) west of the western tip of Cuba, the Miami, Florida-based National Hurricane Center said.
The storm's top sustained winds have dropped to about 85 mph (140 kph). It was moving north-northwest at near 3 mph (6 kph), the Hurricane Center said. Gradual weakening is expected over the next day or so, the forecasters said.
Paula was expected to turn north and east on Thursday, forecasters said.
Cuba has issued a tropical storm warning for the province and city of Havana, and Mexico canceled all warnings on the Yucatan. A hurricane warning was still in effect for Cuba's westernmost province, Pinar del Rio.
A tropical storm watch was issued for the Florida Keys, from Craig Key westward, including the Dry Tortugas, the Hurricane Center said. A tropical storm watch means tropical storm conditions are possible within 48 hours.
Tropical storm-force winds affecting Mexico were forecast to diminish later Wednesday, forecasters said.
Paula tipped the scales into hurricane strength Tuesday and intensified quickly to a Category 2 storm when its sustained winds topped 95 mph.
The storm is forecast to gradually weaken. Track-prediction maps show it becoming a tropical storm over Cuba on Thursday.
The Hurricane Center has described Paula as small. Its hurricane-force winds extend outward only up to 10 miles (16 kilometers) from the center and tropical strength-force winds extend outward up to 60 miles (95 kilometers).
Paula is predicted to drop 3 to 6 inches of rain over parts of western and central Cuba, with maximum amounts of 10 inches in isolated areas. That could cause flash floods and mudslides, the center said.
In addition, a storm surge is forecast to raise water levels by as much as 4 to 6 feet above normal levels along the coast of extreme western Cuba, the Hurricane Center said, accompanied by "large and destructive waves."