"People in that area are still reeling from the effects of Hurricane Charley when 41,000 homes were destroyed. There are lots of people still living in shelters," reports CBS News Producer Portia Siegelbaum in Havana.
There were unconfirmed reports of at least two deaths on Grand Cayman island.
One of the strongest storms on record to hit the region, Ivan has killed at least 65 people across the Caribbean and threatens millions more people in its projected path. About 1.3 million Cubans were evacuated from their homes, most taking refuge in the sturdier homes of relatives, co-workers or neighbors.
"It's as bad as it can possibly get," Justin Uzzell, 35, said Sunday by telephone from his fifth-floor refuge in an office building on Grand Cayman island. "It's a horizontal blizzard," he said, "The air is just foam."
Ivan's sustained winds weakened to 150 mph as they neared the wealthy British territory, then intensified late Sunday as the hurricane headed for western Cuba with winds nearing 160 mph. Storms over 155 miles are Category 5 on the Saffir-Simpson scale, the highest level and capable of catastrophic damage.
Officials had yet to assess damage, but Donnie Ebanks, deputy chairman of the Cayman Islands' National Hurricane Committee, estimated between one-fourth and half of the 15,000 homes in Grand Cayman suffered some damage.
Ivan was projected to pass near or over Cuba's western end by Monday afternoon or evening. The National Hurricane Center in Miami said the storm surge could reach 25 feet with dangerous, battering waves.
The Hurricane Center said ham radio operators on Grand Cayman reported people standing on roofs because the sea in the low-lying island had surged up to 8 feet above normal tide levels.
The eye of the storm did not make a direct hit, passing just south of the island.
Emergency officials said residents from all parts of the island reported blown-off roofs and flooded homes as Ivan's shrieking winds and driving rain lashed Grand Cayman, the largest of three islands in the British territory of 45,000 people, a popular scuba diving destination and banking center.
There were no immediate reports of injuries in the Cayman Islands, but at least 15 were killed in Jamaica, and 39 in Grenada. Ivan also killed five people in Venezuela, one in Tobago, one in Barbados, and four children in the Dominican Republic.
After Cuba, Ivan was projected to move into the Gulf of Mexico Tuesday, nearing parts of Florida's west coast still recovering from Hurricane Charley, on a path toward northwestern Florida.
"It's about 100 miles south-southeast of the western tip of Cuba, moving to the west-northwest, so it may go over the extreme western tip of Cuba, but it also could go right through the Yucatan Channel between Cuba and the Yucatan Peninsula," National Hurricane Center meteorologist Richard Knabb told CBS Radio News.
That means it could make landfall at Mississippi or Louisiana.
"Anywhere from, say, the Tampa area over to Louisiana could see either an indirect or a direct impact from this storm," Knabb said.
Officials in the Panhandle are watching Ivan's every wobble, reports CBS News Correspondent Cami McCormick in Tallahassee. Officials there were expected to decide later Monday whether residents of low-lying areas should evacuate.
Mexico issued a hurricane watch and tropical storm warning for the northeastern Yucatan Peninsula, and hundreds abandoned fishing settlements on the nearby island of Holbox. The resort city of Cancun opened shelters and closed beaches.
While projections had the storm bypassing the Florida Keys, officials kept an evacuation order in place for the island chain's 79,000 residents.
The storm could dump up to one foot of rain that could cause life-threatening flash floods and mudslides, the Hurricane Center said.
In Cuba, the threatened area included Havana, where traffic was light Sunday as most took shelter. The hurricane — being called "Ivan the Terrible" — is the most powerful storm to threaten Cuba since the 1959 revolution brought Fidel Castro to power.
In western Cuba, dozens of families in coastal La Coloma bundled up clothes, medicine, furniture and television sets before boarding buses to find shelter.
"I feel sad leaving my house on its own," said Ricardo Hernandez, 44, a fisherman. "But I have to protect myself and save the lives of my family."
The last Category 5 storm to make landfall in the Caribbean was Hurricane David, which killed more than 1,000 people and devastated the Dominican Republic in 1979, Mojica said.
Only three Category 5 storms are known to have hit the United States. The last was Hurricane Andrew, which hit South Florida in 1992, killing 43 people and causing more than US$30 billion in damage.
Jamaica was saved from a direct hit Saturday but still suffered heavy damage from Ivan.
Waves broke more than 30 feet high in the northwestern resort town of Negril on Sunday, crashing over a seawall and the rooftops of single-story hotel bungalows and restaurants, damaging many. Uprooted palm trees lay atop buildings and against walls, while armed security guards kept watch.
Ivan damaged dozens of homes in Barbados, St. Lucia and St. Vincent before making a direct hit Tuesday on Grenada, which was left a wasteland.
In Miami, storm-weary American medical students arrived home from Grenada, where more than 30 people were killed…
"Pretty much in Grenada, there's nothing really left of it," John Ramano told CBS News. "A lot of it was destroyed. We got through it and I am so excited to be home."
Ivan also destroyed nearly 100 houses and damaged hundreds more in Haiti.