The fearsome core of Hurricane Wilma slammed into the island of Cozumel early Friday, starting a long, grinding march across Mexico's resort-studded coastline, where thousands of stranded tourists hunkered down in shelters and hotel ballrooms. Forecasters at the National Hurricane Center in Miami said the hurricane's eyewall - the fastest-moving section surrounding the eye - had hit Cozumel, a popular stop for divers nad cruise ship passengers where hunhdreds of residents and 970 tourists were riding out the hurricane. The hurricane was expected to make an agonizingly slow journey to the tip of Mexico's Yucatan Peninsula and sideswipe Cuba - 220 kilometers (130 miles) east of Cancun - then swing east toward hurricane-weary Florida. Cuba evacuated nearly 370,000 people in the face of the storm, which has already killed at least 13 people in Haiti and Jamaica. "The most important thing now ... is to protect lives," President Vicente Fox said in a broadcast address to the nation Thursday night. Max Mayfield, director of the National Hurricane Center in Miami said the storm "has the potential to do catastrophic damage." With winds of 230 kph (145 mph), Wilma is more powerful than Hurricane Katrina at the time it plowed into the U.S. Gulf Coast on Aug. 29, killing more than 1,200 people. While the wall of the eye had hit, the hurricane center said that the large, slow-moving center of the storm was still about 80 kilometers (50 miles) southeast of Cozumel. The hurricane was moving toward the northwest at 6 mph (9 kph), which was expected to bring the eye to shore by midday. Forecasters said the storm could dump as much as 40 inches (1 meter) of rain over isolated, mountainous parts of western Cuba and about half that in some other parts of Cuba and the Yucatan Peninsula. Its slow progress delayed its expected arrival in Florida until Monday, but fueled fears that it would have more time to dump rain and pummel the low-lying Mayan Riviera, possibly causing major damage. The hurricane was expected to churn over Mexico's Yucatan Peninsula for most of the weekend. The hurricane's eye is so large it might take hours to pass over land, leading to fears that confused residents might leave shelters in the calm of the middle of the storm. At the beachside Playa Azul hotel on Cozumel's north end, manager Martha Nieto said "the waves are getting very high." "We wish it was over. The waiting drives you to desperation," Nieto said by telephone. After airports closed late Thursday, desperate tourists who had lined up for hours in a failed bid to get on the last planes out were instead shuttled to sweaty emergency shelters. Devon Anderson, 21, from Sacramento, California, was packed into a local school with other Americans. He said the army never arrived to board up the windows. "There's no food, no water," he said. "We've pretty much just been deserted." About 20,000 tourists remained at shelters and hotels on the mainland south of Cancun, and an estimated 10,000 to 12,000 in the city itself. Some, like 30-year-old Carlos Porta of Barcelona, Spain, were handed plastic bags with a pillow and blanket. "From a luxury hotel to a shelter. It makes you angry. But what can you do?" he said. "It's just bad luck." In Cancun, high winds bent palm trees and waves gobbled the city's white-sand beaches. Nearly 50 hotels were evacuated, leaving the normally busy tourist zone deserted. The city of 500,000 people Early Wednesday, Wilma became the most intense hurricane recorded in the Atlantic. The storm's 882 millibars of pressure broke the record low of 888 set by Hurricane Gilbert in 1988. Lower pressure brings faster winds. With Florida the following target, Gov. Jeb Bush declared a state of emergency, and officials cleared tourists out of the exposed Florida Keys. Across Florida's southwest coast, people put up shutters, bought canned goods and bottled water and waited in ever-growing lines at gas stations. In Belize, a nation south of Mexico's Yucatan Peninsula, officials canceled cruise ship visits and tourists were evacuated from islands offshore. But the tiny country weathered the storm with few reports of damage.