KEY WEST, Fla. (AP) - Hurricane Ike grew to fierce Category 4 strength Saturday as it roared on an uncertain path that forced millions from the Caribbean to Florida, and Louisiana to Mexico, to nervously wonder where it would eventually strike.

Preparations stretched more than 1,000 miles as the massive, 135-mph storm took a southwesterly shift that could send it over Cuba and the Florida Keys by Tuesday before heading into the warm open waters of the Gulf of Mexico. And once again, a possible target was New Orleans and the already storm-weary U.S. Gulf Coast.

"These storms have a mind of their own," Florida Gov. Charlie Crist said after a meeting with mayors and emergency officials. "There are no rules, so what we have to do is be prepared, be smart, vigilant and alert."

First in Ike's path was the low-lying British territory of Turks and Caicos, already pummeled for four days this week by Tropical Storm Hanna. At the airport in Providenciales, Patrick Munroe had hoped to catch a departing flight, but was turned away, even before the airport shuttered.

"It looks really, really serious," he said. "And I think it's going to be devastating."

In Haiti, authorities tried to move thousands of people into shelters ahead of Ike, while they still struggled to recover from Tropical Storm Hanna. Rescue workers feared Hanna's death toll could rise into the hundreds in the flooded city of Gonaives and that aid efforts could be further impeded as Ike approached.

Hanna did not pack the same punch Saturday while racing up the U.S. Eastern seaboard, but did cause one death in a traffic accident on Interstate 95 in Maryland. It also brought fits of wind and pelting rain on its trek toward New England.

But Ike is another matter.

Tens of millions of people in countries spread over a swath of the hurricane zone monitored the trajectory of a storm that had a huge footprint, with tropical storm-force winds stretching up to 140 miles from its eye.

At 4 p.m. EDT, Ike's center was located about 90 miles east of Grand Turk Island as the storm moved west-southwest at about 15 mph, the National Hurricane Center in Miami said.

Forecasters said Ike was gaining strength over warm water, its maximum winds increasing to Category 4, 135 mph Saturday, up from a Category 3 storm packing 115-mph winds hours earlier.

Tourists were urged to leave the Bahamas, and authorities in the Dominican Republic began evacuating dozens of families who live on the banks of a river that could flood with waters from two already overfilled dams.

In Cuba, the island's top meteorologist warned Ike was a "true danger" and government officials began the early phases of emergency preparations. But no alarm was evident in Havana, where the U.S. soccer team was set to play Cuba in a World Cup qualifying match.

In Louisiana, still recovering from last week's Hurricane Gustav, Gov. Bobby Jindal set up a task force to prepare for the possibility of a new round of havoc.

"We're not hoping for another strike, another storm, but we're ready," he said.

In Florida, batteries, water and gas cans became major commodities, as nearly the entire state appeared within the cone of areas that might be hit.

Jose Calbo planned to fly to Chicago later Saturday with his girlfriend, leaving his Miami-area home behind.

"Why be here without power and lights?" he asked. "There is nothing you can do. The best thing you can hope for is to board up the house, empty the freezer."

Visitors to the Florida Keys were under a mandatory evacuation order Saturday and a light but steady stream of traffic rolled out of Key West ahead of the storm. In typical fashion, laid-back residents and business owners kept their shops, bars and restaurants open. But unique was the worry, still nearly four days ahead of potential landfall.

Jesse Damian hammered plywood over windows at The Bike Shop.

"The owners are usually like all the people who wait until the last minute around here," he said. "But this one's looking pretty bad."

Key West was last seriously affected by a hurricane in 2005, when Category 3 Wilma sped past. The town escaped widespread wind damage, but a storm surge flooded hundreds of homes and some businesses.

The deadliest storm to hit the island was a Category 4 in 1919 that killed up to 900 people, many of them offshore on ships that sank. A shrine built by nuns in 1922 known as The Grotto pays tribute to the victims, with an etched stone that reads, "As long as the Grotto stands, Key West will never again experience the full brunt of a hurricane."

Many believe the invocation has worked, though in 1998, Hurricane Georges directly hit Key West, damaging hundreds of homes with 105 mph winds.

But many residents are so used to the storm warnings that they took it all in stride.

Dennis Joseph, 47, of Miami Beach, already had accordion shutters on his home Saturday and stocked up on food and water. He went to a Home Depot store in search of a solar-powered radio, but said he won't evacuate unless Ike strengthens into a Category 4, which has winds from 131 mph to 155 mph.

"I'm from Miami, so I'm familiar,"he said. "I'm desensitized."

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Contributing to this report were Associated Press writers Matt Sedensky, Suzette Laboy, Brendan Farrington and Lisa Orkin in Miami, Sarah Larimer in Homestead, Fla.; Steve Szkotak in Virginia Beach, Va.; Melinda Deslatte in Baton Rouge, La.; Ben Fox in Providenciales, Turks and Caicos; Mike Melia in Nassau, Bahamas; Anita Snow in Havana; and Jonathan Katz in Gonaives, Haiti.