Paloma made landfall near Santa Cruz del Sur late Saturday as an extremely dangerous Category 4 storm, but soon weakened to a tropical storm with winds of 70 mph (110 kph), according to the National Hurricane Center in Miami. Forecasters say the Cuban government has discontinued all warnings associated with Paloma.
The storm was expected to continue to lose strength as it slowly moved across Cuba and headed toward the central Bahamas on Monday morning. The storm was expected to unravel and not threaten the southern tip of Florida.
In the central-eastern Cuban province of Camaguey, more than 220,000 people were evacuated from low-lying areas. Another 170,000 people were moved in the eastern province of Las Tunas.
Cuba regularly relocates masses of people to higher ground ahead of tropical storms and hurricanes, preventing major losses of life.
In the city of Camaguey, 79-year-old Rosa Perez waited out the storm at a government shelter with her 83-year-old husband and about 900 others from the town of Santa Cruz del Sur.
Perez was a toddler when she watched as her mother, older sister and about 40 other relatives were swept away in a storm surge during a 1932 hurricane that killed about 3,000 people.
"We're just waiting to see what happens to our home and our beach," she said.
Fellow Santa Cruz del Sur resident Aida Perez, who is not related, watched the news with her daughters, ages 19 and 10.
"This is a really hard blow," the 44-year-old said. She was certain they would lose their home and everything in it. "What's important is that we are alive."
Outside on the nearly deserted, flooded streets, four men struggled in pouring rain to carry a refrigerator to a more secure building.
At 7 a.m. EST Sunday, Paloma was near Camaguey. Once packing winds of 145 mph, the storm had slowed over land and was moving northeast at about 5 mph (7 kph).
Tropical storm force winds extended outward up to 115 miles (185 km).
In an essay published in state media Saturday, former President Fidel Castro warned that Paloma could slow Cuba's recovery from hurricanes Gustav and Ike, which hit in late August and September causing about $9.4 billion in damage and destroying nearly a third of the island's crops.
The hurricane center said Paloma could bring parts of the island battering waves and a life-threatening storm surge of up to 23 feet (7 meters).
Elsewhere, Paloma knocked out power across much of Grand Cayman island, downing trees, flooding low-lying areas and ripping off roofs. But residents appeared unscathed as businesses reopened and electricity and water service were restored Saturday.
Donovan Ebanks, chairman of the Hazard Management Committee, said no injuries were reported.
"There has been minimal, if any, damage on Grand Cayman," Ebanks said.
Paloma's fierce winds ripped the roofs off some buildings on Cayman Brac, to the east.
Associated Press writers Anita Snow in Havana and Trent Jacobs in George Town, Cayman Islands, contributed to this report.