The hurricane was projected to plow into the oil-rich Gulf of Mexico at full force Sunday, and reach the U.S. coast as early as Monday afternoon. A hurricane watch was issued from Texas east to Florida, an area that includes New Orleans, which Hurricane Katrina devastated in 2005.
More than a million Americans took buses, trains, planes and cars as they streamed out of New Orleans and other coastal cities, where Katrina killed about 1,600 people.
Gustav already has killed 81 people by triggering floods and landslides in other Caribbean nations.
The storm knocked power out in many parts of Cuba's capital, Havana, as shrieking winds blasted sheets of rain sideways though the streets and whipped angry waves against the famed seaside Malecon boulevard. Felled tree branches and large chunks of muddy earth littered crowded roads.
The U.S. National Hurricane Center said Gustav had sustained winds of 150 mph (240 kph) -- with higher gusts -- as the heart of the storm began hitting Cuba's outlying island province of Isla de Juventud, where officials cut power to many areas. A Category 5 hurricane has winds above 155 mph (249 kph).
"The rain is not so intense, but there is a lot, a lot of wind," said Isabel Alarcon from Nueva Gerona, the largest city on the island of 87,000 people. "The officials, they have told us the wind will be bad first but then the rain could cause flooding into the night."
Gustav toppled mango and almond trees on the Isla de Juventud and was beginning to peel back the tin roofs of some houses.
"People are calm, but things are getting ugly," Ofilia Hernandez, another Nueva Gerona resident, said by telephone.
The government said it had evacuated some 190,000 people from low-lying parts of westernmost Cuba, Pinar del Rio province, where the tobacco for the island's famed cigars is grown. Officials reported that 50,000 people had been moved to higher ground farther east.
Cuba grounded all domestic flights and halted all buses and trains to and from Havana, where some shuttered stores had hand-scrawled "closed for evacuation" signs plastered to their doors.
Authorities boarded up banks, restaurants and hotels, and residents nailed bits of plywood to the windows and doors of their houses and apartments.
"It's very big and we've got to get ready for what's coming," said Jesus Hernandez, a 60-year-old retiree who was using an electric drill to reinforce the roof of his rickety front porch.
The government announced it was stepping up emergency production of bread at state-run bakeries and lines formed all over the city as Cubans waited for loaves.
In tourist-friendly Old Havana, heavy winds and rain battered crumbling historic buildings. There were no immediate reports of major damage, but a scaffolding erected against a building adjacent to the Plaza de Armas was leaning at a dangerous angle.
Lidia Morral and her husband were visiting Cuba from Barcelona. She said Gustav forced officials to close the beaches the couple wanted to visit in Santiago, on the island's eastern tip. The storm also prevented them from catching a ferry from Havana to the Isla de la Juventud on Saturday.
"It's been following us all over Cuba, ruining our vacation," said Morral, who was in line at a travel agency, trying to make other plans. "They have closed everything, hotels, restaurants, bars, museums. There's not much to do but wait."
By late Saturday afternoon, Gustav was about 80 miles (135 kilometers) south-southwest of Havana and it was moving northwest near 15 mph (24 kph).
Hurricane force winds extended out 70 miles (110 kilometers) in some places.
The U.S. naval base at Guantanamo, Cuba, was hundreds of miles (kilometers) to the east, out of the storm's path.
Gustav rolled over the Cayman Islands Friday with fierce winds that tore down trees and power lines while destroying docks and tossing boats ashore, but there was little major damage and no deaths were reported.
Haiti's Interior Ministry on Saturday raised the hurricane death toll there to 66 from 59 and Jamaica raised its count to seven from four. Gustav also killed eight people in the Dominican Republic early in the week.
Meanwhile, the hurricane center said Tropical Storm Hanna was projected to near the Turks and Caicos Islands late Sunday or on Monday, then curl through the Bahamas by early next week before possibly threatening Cuba.
As it spun over open waters, Hanna had sustained winds near 50 mph (85 kph) late Saturday afternoon and the hurricane center warned that it could kick up dangerous rip currents along parts of the southeastern U.S. coast.