The rapidly strengthening storm was almost a hurricane by late Monday with winds of 70 mph (110 kph) and was expected to slam into Haiti on Tuesday afternoon, the National Hurricane Center in Miami said. A hurricane has winds of at least 74 miles (119 kph).
Forecasters said storm preparations in Haiti should be rushed to completion and that floods and landslides were possible across its southern peninsula. The forecasts suggested Gustav's eye could pass near the capital of Port-au-Prince, home to nearly 3 million people.
On Monday evening, the storm was centered about 150 miles (240 kilometers) south-southeast of Port-au-Prince and was heading toward the northwest at near 12 mph (19 kph).
Carnival Cruise Lines diverted one of its ships to a Mexican port instead of Montego Bay, Jamaica, to avoid the storm, company spokesman Vance Gulliksen said. Other cruise lines said they were closely tracking the storm's path.
After passing over Haiti, Gustav was expected to hit Cuba's southeastern tip on Wednesday.
The commander of the Guantanamo military base in Cuba, where the U.S. holds about 265 men, many suspected of belonging to al-Qaida or the Taliban, ordered U.S. military personnel to prepare for the storm to hit late Tuesday or early Wednesday.
"We're monitoring the track of ... Gustav and reviewing our destructive weather plans and procedures," said Army Maj. Richard Morehouse, a spokesman for detention operations at the base.
Vulnerable to high winds are dozens of tents pitched on an abandoned runway where those attending war-crimes trials for alleged terrorists are housed. No hearings are scheduled this week.
Morehouse told The Associated Press that the lockups housing all detainees "are capable of withstanding hurricane force winds and rain."
Haitians were told to stay on alert for evacuations and to avoid crossing flooded rivers, the cause of nearly all 23 deaths on the greater island of Hispaniola during last week's Tropical Storm Fay.
The agricultural ministry, already dealing with a food crisis and fighting to raise national production, advised farmers to put livestock in safe locations. All maritime activities also were suspended until further notice.
Few people in Haiti's capital appeared to be aware of the brewing storm as rumors spread of new protests against high food and education prices planned for this week. Haitian radio reported that a handful of protesters burned tires Monday in Les Cayes, a town in the southwest.
"I didn't know there was a tropical storm coming," said Dunis Amilca, a 29-year-old resident of the oceanside Port-au-Prince slum of Cite Soleil. "I'm just going to stay in my house and watch out for it."
Dominican authorities also issued storm warnings and advised small boats to remain in port, even on the north side of the island of 17 million people.
Meanwhile, two other storms were lashing the southeastern U.S. and Mexico's Pacific coast.
The remnants of Fay brought heavy rain and winds from Georgia to Louisiana. Floridians were still mopping up floodwaters from a storm that stuck around for a week and made a historic four landfalls, dumping more than 30 inches (76 centimeters) of rain along the central Atlantic coast.
The National Weather Service said the vestiges of Fay would deluge northern Georgia on Monday and Tuesday with 3 inches (8 centimeters) to 5 inches (13 centimeters) of rain expected in the Atlanta area and up to 8 inches (20 centimeters) in northeast Georgia. In Alabama, flash flood and tornado warnings were posted.
In Mexico, Tropical Depression Julio dumped rain on the central Baja California peninsula before heading toward the northern Gulf of California.
The hurricane center said late Monday that Julio was downgraded from a tropical storm to a tropical depression. The Mexican government lifted all tropical storm warnings.
Julio caused little major damage but forecasters said it could drench the U.S. Southwest with rain in the coming days.
The National Hurricane Center said Julio was located about 55 miles (85 kilometers) north-northwest of Santa Rosalia, Mexico, and was moving north-northwest at near 7 mph (14 kph).
