Miami, Florida (CNN) -- Tropical Storm Paula pushed across western Cuba Thursday evening with wind gusts just under hurricane strength in some places, bringing heavy rain and high winds to the island nation, forecasters said.
The storm is gradually weakening and is expected to become a tropical depression Friday, the Miami, Florida-based National Hurricane Center said
As of 8 p.m. ET, the center of Paula was about 25 miles (45 kilometers) east of Havana, the center said. It was moving east at 14 mph (22 kph).
Paula passed just south of the Cuban capital around 6 p.m. Thursday -- with sustained winds of 41 mph (67 kph) and a gust of 54 mph (87 kph) recorded in Havana -- after making landfall at about noon near Puerto Esperanza.
The storm's maximum sustained winds have weakened to 55 mph (90 kph), the center said Thursday night, but wind gusts of 68 mph had been recorded earlier near Puerto Esperanza. Stronger gusts were confined to a small area near the storm's center, the center said.
Paula's tropical storm-force winds have expanded to 70 miles (110 km) outward from the center, altering the landscape of a storm that has been roughly half that size for most of its duration.
Forecasters said the storm was likely to stick to an east to east-northeast track, moving across western and central Cuba Thursday night and Friday.
The hurricane center said that tropical storm force winds should continue to spread eastward across western and central Cuba Thursday night, primarily along the north coast.
The center discontinued an earlier tropical storm watch also was for the Florida Keys and Dry Tortugas.
Emergency management officials in the Keys said Wednesday they were keeping an eye on the progress of Paula and expected some gusty winds and rain, but no protective actions had been initiated. Forecasters predict the center of Paula will remain south of the Keys.
Paula is likely to dump an additional 2 to 4 inches of rain over portions of western and central Cuba over the next two days, the National Hurricane Center said. Total maximum amounts could be 10 inches in some areas. Heavy rain could trigger flash floods and mudslides, forecasters said. The Florida Keys could see between 1 and 2 inches of rain.
In addition, a storm surge is forecast to raise water levels by 2 to 4 feet above normal tide levels along the coast of western Cuba, accompanied by "large and destructive waves," the hurricane center said.