Gustav's is expected to plow into Cuba with winds of 115 mph before it barrels into the U.S. Gulf Coast next week, three years after Hurricane Katrina.
The U.S. National Hurricane Center in Miami called the storm "dangerous" and said it had reached the status of a major hurricane, the second one of this Atlantic season after Bertha in July.
Gustav, which killed 71 people in the Caribbean, rolled over the Cayman Islands Friday with fierce winds that tore down trees and power lines. It was expected to cross Cuba's cigar country Saturday and head into the Gulf of Mexico by Sunday.
Gustav first struck Cayman Brac and Little Cayman, the smaller easternmost "Sister Islands" in the chain. Storm surge and heavy rains flooded the streets.
Two people were knocked down by huge waves as they tried to take pictures of the storm on Little Cayman, but there were no other immediate reports of injuries, said Hemant Balgobin, disaster manager for the Red Cross in the British territory.
There were reports of damaged homes in Cayman Brac and flooding throughout the islands but authorities had not yet fully assessed the situation, said Balgobin, who was on Grand Cayman, the largest in the chain.
"Things weren't really as bad as they could have been," he said.
More than 1,100 people spent the night in government shelters in the three islands as high waves and heavy winds battered the chain, the National Emergency Operations Center said in a statement. Most people hunkered down in private homes or hotels.
By 5 a.m. EDT Saturday, Gustav's eye had left the Caymans behind and was about 255 miles east-southeast of the western tip of Cuba. It was moving northwest near 12 mph.
Caymans authorities did not impose a curfew but urged people to remain indoors to avoid interfering with emergency workers.
Hotels asked guests to leave and, after the airport closed, prepared to shelter those who remained. Chris Smith, of Frederick, Maryland, said his hotel handed out wrist bands marked with guests' names and room numbers so that "if something happens they can quickly identify us."
"That was a little bit sobering," he said, standing outside the hotel with his luggage.
The storm killed four people in a daylong march across the length of Jamaica, where it ripped off roofs and downed power lines. About 4,000 people were displaced from their homes, with about half relocated to shelters. Prime Minister Bruce Golding said the government sent helicopters Friday to rescue 31 people trapped by floods.
At least 59 people died in Haiti and eight in the Dominican Republic.
Gustav could strike the U.S. Gulf coast anywhere from the Florida Panhandle to Texas, but forecasters said there is a better-than-even chance that New Orleans will get slammed by at least tropical-storm-force winds.
As much as 80 percent of the Gulf of Mexico's oil and gas production could be shut down as a precaution if Gustav enters as a major storm, weather research firm Planalytics predicted. Oil companies have already evacuated hundreds of workers from offshore platforms.
Retail gas prices rose Friday for the first time in 43 days as analysts warned that a direct hit on Gulf energy infrastructure could send pump prices hurtling toward $5 a gallon. Crude oil prices ended slightly lower in a volatile session as some traders feared supply disruptions and others bet the U.S. government will release supplies from the Strategic Petroleum Reserve.
Gustav was projected to hit Cuba's Isle of Youth, then cross the main island into the Gulf of Mexico by Sunday. Cuban state television announced that effective Saturday, all buses and trains to and from Havana will be suspended until further notice.
Meanwhile, Tropical Storm Hanna was projected to curl westward into the Bahamas by early next week. It had sustained winds near 50 mph early Saturday.
Along the U.S. Gulf Coast, most commemorations of the Katrina anniversary were canceled because of Gustav, but in New Orleans a horse-drawn carriage took the bodies of Katrina's last seven unclaimed victims to burial.
President Bush declared an emergency in Louisiana, a move that allows the federal government to coordinate disaster relief and provide assistance in storm-affected areas.
New Orleans Mayor Ray Nagin said an evacuation order was likely, though not before Saturday, and the Federal Emergency Management Agency said it expects a "huge number" of Gulf Coast residents will be told to leave the region this weekend.