Ivan, blamed for the deaths of at least 44 people - most of them when it ravaged Grenada - was upgraded on Saturday to a rare, top-intensity Category 5 hurricane as it headed towards the Cayman Islands and Cuba.
Packing winds of 270kph, the hurricane wrecked houses and washed away roads in Jamaica. It is forecast to strike Florida early next week.
Ivan ripped off roofs across Jamaica and torrential rains triggered mudslides, washing out roads. The storm brought trees and poles crashing down in capital Kingston, where ravines overflowed and flooded streets.
Jamaica's toll rose to 16 and included people whose houses collapsed when trees fell on them and others who drowned when their homes were submerged by floodwaters.
Jamaican police made 28 arrests as they battled looting that erupted in the storm's wake. Two men were shot to death by police in gunfights when officers tried to retrieve stolen goods.
Robbers held up emergency workers at gunpoint, shooting and injuring one doctor as she slowed her car in rising water.
The storm is on course to hit the Cayman Islands, a wealthy British colony northwest of Jamaica and Cuba.
It also threatens Florida with its third big hurricane strike in a month, after Charley and Frances caused an estimated $9.4 billion to $11.4 billion in insured damages.