KINGSTON, Jamaica — Residents, tourists and oil workers fled as the winds and rain of Gustav swamped Jamaica on Thursday, leaving 59 people dead in its wake. Louisiana and Texas put their national guards on standby, and New Orleans said a mandatory evacuation might be necessary.

At least 51 people died in Haiti from floods, mudslides and falling trees, including 25 around the city of Jacmel, where Gustav first struck land Tuesday. Eight more people were buried when a cliff gave way in the Dominican Republic. Marcelina Feliz died clutching her 11-month-old baby, and five more children were smothered in the wreckage beside her.

Late Thursday, Gustav’s center was 15 miles east-northeast of Kingston, Jamaica’s low-lying capital. Forecasters said it could grow to a hurricane before slamming into Grand Cayman tonight.

Even as tourists searched for flights off the islands, officials urged calm. Theresa Foster, one of the owners of the Grand Caymanian Resort, said Gustav didn’t look as threatening as Hurricane Ivan, which destroyed 70 percent of Grand Cayman’s buildings four years ago.

“Whatever was going to blow away has already blown away,” she said.

Forecasters said parts of Jamaica could get 25 inches of rain, which could trigger landslides and cause serious crop damage. Authorities told fisherman to stay ashore, and hotel workers secured beach umbrellas in the resort city of Montego Bay.

Jamaica evacuated low-lying areas including Portmore, a crowded and flood-prone area outside Kingston. Kingston’s main airport was closed and buses stopped running even as people streamed into supermarkets for emergency supplies and men played dominoes in bars.

Oil prices spiked above $120 a barrel before settling below $116 in a session made volatile by fears that the storm could affect production in the Gulf area, home to 4,000 oil rigs and half of America’s refining capacity. Hundreds of offshore workers pulled out, and analysts said the storm could send U.S. gas prices back over $4 a gallon.