MIAMI, Florida (CNN) -- Gustav's top winds got up to 115 mph (185 kph) Saturday morning, raising the storm to Category 3 status, according to the National Hurricane Center.
Hurricane Gustav is expected to pass over the western tip of Cuba later Saturday as it moves into the northwestern Caribbean.
Forecasters warn Gustav could grow to be a Category 4 hurricane as it barrels toward the U.S. Gulf Coast for a landfall late Monday or Tuesday.
Gustav is the second major hurricane of the 2008 Atlantic hurricane season.
Hurricanes are ranked 1-5 in intensity on the Saffir-Simpson scale. A Category 3 hurricane has sustained winds from 111 to 130 mph and is capable of causing extensive damage. A Category 4 has winds of 131 to 155 mph and can cause extreme damage.
As of 5 a.m. ET, Gustav was about 255 miles (410 kilometers) east-southeast of the western tip of Cuba.
Fear and uncertainty about Gustav's position and strength by Monday sent emergency officials and politicians in the United States scrambling to prepare for a possible landfall somewhere along the Gulf Coast.
In New Orleans, which has yet to fully recover from Hurricane Katrina, Mayor C. Ray Nagin urged people living in FEMA units to make evacuation plans in case they're ordered to leave.
Mississippi Gov. Haley Barbour said Hurricane Katrina victims living in government-issued trailers or mobile homes along his state's coast will begin evacuating this weekend.
Both Louisiana and Mississippi are still recovering from Hurricane Katrina, which killed more than 1,800 people when it slammed ashore near the state line on August 29, 2005.
The hurricane center's five-day forecast places a possible landfall anywhere from Galveston, Texas, eastward to Mobile, Alabama. New Orleans is at the center of the projected path.
New Orleans officials warned residents that they'll be on their own if they ignore orders from police with bullhorns directing them to evacuate, The Associated Press reported.
Jerry Sneed, the city's emergency preparedness director, said the Superdome would be locked and there would be no shelter of last resort if residents decided to accept "all responsibility for themselves and their loved ones," the AP reported.
Gustav caused little damage on Grand Cayman Friday night, according to an official at the Island's airport.
Earlier in the day, the storm blasted Jamaica, killing four people as it downed trees and damaged homes, the National Emergency Operations Center there said.
"It is total devastation everywhere," the councilor for the Manchioneal division, Alston Hunter, told the Jamaican Gleaner newspaper. "Several residents are now crammed into disaster shelters here in east Portland, and the weather continues to make the situation worse."
Even as it moved away from Jamaica, Gustav was dumping rain, possibly 6 to 12 inches of it, on the island, according to the National Hurricane Center. The Cayman Islands and western Cuba were likely to get that much rain as well, with 25 inches possible in some regions.
"These rains will likely produce life-threatening flash floods and mudslides," the center said. The forecasters said coastal storm surge flooding of 2 to 5 feet above normal tide levels could happen in the Cayman Islands and 8 to 13 feet above normal levels in western Cuba, near the center of Gustav as it passes.
Meanwhile, Tropical Storm Hanna passed north of the Leeward Islands Friday with maximum sustained winds of 50 mph (80 kph), the center said.
The center predicted gradual strengthening, and Hanna could be near hurricane strength on Sunday.
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