Cancun, Mexico ? Tropical Storm Claudette lost steam late Thursday as it headed toward the resort island of Cozumel.

Even so, Claudette could still bring battering waves and heavy rain to the Yucatan Peninsula coast. The storm’s center was expected to move over the peninsula by early today, the National Hurricane Center in Miami said.

Mexican authorities lowered their hurricane warning to a tropical storm warning for the entire length of the eastern Yucatan Peninsula, including Cozumel and Cancun.

The storm’s maximum sustained winds slowed to about 70 mph with higher gusts as it drew to within about 80 miles of Cozumel, moving northwest at 14 mph.

Tropical storm-force winds extended up to 140 miles from the center of Claudette. Authorities in Cozumel and Cancun decided not to evacuate tourists, but civil defense officials in Tulum, about 80 miles farther south, advised hotel owners to evacuate guests staying at beach-side cabins.

About 25 guests were asked to leave the wood-and-thatch huts at Tulum’s hotel El Mirador, said manager Asael Concha. Hotel employees also put away wooden beach furniture to prevent injuries in case of high winds.

As the storm neared the coast, disappointed backpackers showed up only to be told they’d have to look for lodging further inland.

“We would like to stay here, but it’s not possible,” said Julia Petschnigg, 23, a student from Austria, as she sat with her backpack at the Mirador hotel.

Tourists watch the clouds over the sea at a Cancun beach in Mexico. Tropical Storm Claudette churned Thursday toward Mexico's Yucatan Peninsula, threatening to plow into the resort city popular with tourists.

Halfway up the coast toward Cancun, employees at the Los Tres Nietos supermarket in the city of Playa de Carmen reinforced the front windows of the store, about five blocks from the beach, with long strips masking tape. Others loaded up on supplies.

There were few signs of storm preparations in Cancun, where winds whipped palm trees and sent newspapers flying across the peninsula’s main highway.

A light drizzle fell on workers securing porch awnings and ceiling fans at the Dadyrock Club disco, which planned to stay open during the storm.

The threatening weather didn’t deter animal trainer Jose Lopez, who stood on a street corner and charged tourists $1.50 for photos with his three squirrel monkeys. He planned to stay out as long as people keep strolling by.

No flights had been delayed or canceled at Cancun’s airport Thursday, airport spokesman Eduardo Rivadeneyra said.

Claudette, the third tropical storm of the Atlantic hurricane season, developed Tuesday in the Caribbean. Before heading toward Mexico it brushed Jamaica’s southern coast with heavy rain and rough surf, battered the Cayman Islands with dangerous waves and above-normal tides and scattered rain over parts of Cuba.

Royal Caribbean International diverted three cruise ships because of the storm, spokesman Michael Sheehan said.

Experts have predicted a busy Atlantic hurricane season, which began June 1 and ends Nov. 30.