(CNN) -- Hurricane Ike continued to batter Cuba with near 80 mph winds Monday night and was expected to gain strength as it barreled toward the Texas-Louisiana border, the National Hurricane Center said.
After leaving Cuba, Ike could make landfall along the middle Texas coast later this week, forecasters said. But Ike could make landfall anywhere from northern Mexico to southern Louisiana.
"It would be difficult to get people to move again for Ike after so many evacuated for Gustav," New Orleans Mayor Ray Nagin said Monday. "People are so weary and so financially tapped."
The forecast path takes it well south of the Florida Keys, and a hurricane watch for the island chain has been discontinued.
Hurricane Ike has weakened to a Category 1 storm with maximum winds of 80 mph, National Hurricane Center forecasters said in an 11 p.m. advisory from Miami, Florida.
Ike's eye is expected to move into the Gulf of Mexico and grow in intensity.
At 11 p.m., Ike's center was 20 miles southeast of Playa Giron on the south coast of Cuba and 140 miles southeast of Havana.
Forecasters said it is too soon to know where Ike might hit along the U.S. Gulf Coast.
Earlier Monday afternoon, Ike's eye had moved back over water off Cuba's southern coast, according to the hurricane center.
Monroe County, Florida, which includes the Florida Keys, said its mandatory evacuation order for residents expired at noon Monday. But officials advised the 18,000 residents who left not to return until Wednesday, when any tropical winds from Ike's outer bands would have passed and essential services would have been fully restored.
Mayor Lyda Ann Thomas of Galveston, Texas, warned residents to stock up on nonperishable items including pet food and diapers and to prepare for going without electricity.
She expects landfall Friday or Saturday in Galveston but said she has not ordered evacuation as of Monday night.
Ike has already punched Cuba, where organized evacuations appeared to save lives, with only four deaths reported from the storm, according to The Associated Press. The Cuban Civil Defense brought buses or trucks to take people to shelters.
Cuban state television reported that two people were killed when they tried to remove an antenna. One man died when a tree crashed into his home, and a woman died when her home's roof collapsed, the AP said.
Ike hit Haiti hard, killing more than 300 people, according to AP.
At least 73 people in Haiti were killed by rains and flooding from the outer bands of Hurricane Ike. Heavy rain from other recent hurricanes have caused flooding and landslides, and 167 deaths were reported after Hurricane Gustav and Tropical Storm Hannah.
Sunday night, waves as high as 50 feet crashed ashore in Baracoa, Cuba, southeast of where Ike made its Cuba landfall as a Category 3 storm. At least 1,000 homes were damaged or destroyed as the sea surge moved into the city, witnesses said.
An estimated 900,000 people left their homes ahead of Ike's arrival and went inland or to higher ground. Some of the evacuees were already homeless after Hurricane Gustav pounded western Cuba last week.
Residents on the western half of the island scrambled to get necessities before the worst of the storm hit, CNN's Morgan Neill reported from Havana, where the winds were picking up and the water was becoming choppy Monday morning, sending growing waves over the city's historic seawall.
Coastal storm surge flooding of 4-7 feet above normal tide levels and rainfall accumulations of 6 to 12 inches were possible in Cuba, the hurricane center said.
People in the capital were worried that Ike's heavy rain would bring flooding and landslides to that area, and damage some of its more fragile infrastructure.
"Some of the old, colonial construction in Havana loses chunks of concrete even in heavy rains," Neill reported.
Many evacuees went to schools or government buildings with stronger roofs. The Cuban government cut power to the eastern half of the island before Ike arrived and canceled all domestic flights.
At Guantanamo Bay Naval Base on Cuba's southeastern tip, the rain was dying down at mid-morning Monday, said Petty Officer Robert Lamb.
"I think we fared pretty well down here," he told CNN by telephone.
Some limbs were down and a few street signs had gotten knocked over, Lamb said, and assessment teams were combing the base to check for any further damage.
"We were prepared for worse than we received," he said.
In Varadero, a hugely popular tourist resort on Cuba's northern central coast, 9,000 tourists were evacuated ahead of Ike's arrival.
Officials predicted the storm -- coming on the heels of Gustav -- could have a devastating impact on the small country's economy.
Nickel mines and sugar plantations, as well as the tourist trade, will suffer from the heavy rain and wind.
Furious wind, rain and the sea surge from Hurricane Ike destroyed or damaged at least 90 percent of the homes this weekend on Grand Turk, the capital island in the Turks and Caicos Islands, according to journalist Audley Astwood.
"It pretty much looks like an episode of 'The Twilight Zone,'" Astwood said. "It's like the end of the world."
The U.S. Navy's USS Kearsarge arrived in the waters off Haiti Monday to support the U.S. Agency for International Development's efforts to assist after the devastation there.
The vessel will assist in moving cargo and equipment between affected cities and will deliver relief supplies, said a statement from the U.S. Naval Forces Southern Command.
Britain's Royal Navy sent the HMS Iron Duke to the Turks and Caicos Islands -- a British territory -- to deploy first aid and rescue teams, a statement from the British military said.
Authorities evacuated the Florida Keys over the weekend in case Ike's path veered northward.
In Louisiana, Gov. Bobby Jindal pre-emptively issued a state of emergency. More than 370,000 people remain without power in the state, nearly a week after Gustav made landfall, he said.
"Like I told you before Gustav, let's hope it's all a false alarm," he said. "There continues to be much uncertainty about [Ike's] predicted track."
CNN's Karl Penhaul, Morgan Neil and April Williams contributed to this report.