Hurricane Dean has been pounding offshore oil and gas platforms in the Gulf of Mexico, after weakening as it crossed the Yucatan peninsula.
The facilities were shut and workers evacuated before the storm arrived.
Earlier, the hurricane toppled trees and houses on the Mexican peninsula and in the neighbouring country of Belize, bringing torrential rain.
Dean was a Category Five hurricane, the highest level, when it made landfall, but later weakened to Category One.
It should strengthen as it crosses the Gulf of Mexico to make landfall again.
Major tourist resorts were not directly hit, but indigenous Mayan villages were exposed to its full force. There are no reports of deaths in Mexico so far.
At 0900 GMT, Dean was moving north-west across the gulf with winds of 80mph (130km/h).
Dean is expected to hit Mexico again at about 1300 (1800 GMT) on Wednesday between Veracruz and Tampico.
US National Hurricane Center (UHC) spokesman Jamie Rhome warned residents not to let their guard down before Dean's return.
"We often see that when a storm weakens, people let down their guard completely. You shouldn't do that," he told Associated Press news agency.
The eye of the storm came ashore over the Yucatan Peninsula, about 170 miles (270km) south of Cancun, early on Tuesday in a sparsely populated area near the town of Majahual, where hundreds of homes were destroyed.
It lashed low-lying Mayan communities, and rain, poor communications and impassable roads made it hard to establish how they had fared in the storm.
President Felipe Calderon, who has cut short his visit to Canada for the Nafta summit, went to the affected areas. He said relief efforts would focus on these communities.
Ancient Mayan ruins were also in the hurricane's path, but officials from Mexico's National Anthropology and History Institute told AP that none of the archaeological sites in Quintana Roo and Yucatan were damaged.
Andrea Montalvo, of the US-based Spanish-language Telemundo television network, said the storm was wreaking havoc in the town of Chetumal, to the east of Majahual.
"Inside the hotel it is really bad, every 10 or 15 minutes you can hear windows shattering and people are coming out of their rooms in panic," she said.
"If this is how it is here in this hotel, which is pretty solid, I don't want to think about how it is there."
City officials said there were power cuts as the wind knocked over trees and sent debris flying through the air.
Further south, most of Belize was without power. Officials in Belize City closed hospitals and urged people to head inland, saying the town's shelters were not strong enough.
US President George W Bush offered aid to help hurricane victims, saying: "We stand ready to help".
"The American people care a lot about the human condition in our neighbourhood, and when we see human suffering we want to do what we can," he said.
Fleeing the storm
The hurricane has already claimed at least 12 lives in the eastern Caribbean.
Jamaica postponed its general election, due to be held on 27 August, until 3 September, after the storm passed just to the south of the island leaving at least three people dead.
About two-thirds of the tourists in Cancun and other resorts left the area before Dean's arrival, but most resorts were spared the worst effects of the hurricane.
Dean is thought to have been less damaging than the Category Five Hurricane Wilma in 2005, which lingered over the Yucatan for a day, killing 10 people and wrecking large areas of Cancun.
It is the third strongest Atlantic hurricane to make landfall since records began in the 1850s.