Tropical Storm Alex has moved into the Gulf of Mexico after dumping rains that left at least four people dead.

The storm, centred about 90 kilometers south-southwest of Campeche, Mexico on Sunday afternoon, is tracking west-northwest at approximately 15 kph.

That means, for now, the first named storm of the season is not taking direct aim at the massive Gulf oil spill, but the U.S. Coast Guard says the storm could change course and speed up by mid-week.

However, if Tropical Storm Alex does become a hurricane in the coming days, it will be far from the BP oil leak.

The storm hit Belize's coast late Saturday with 100 km/h winds and torrential rain. Roughly 1,400 people fled the island resort of San Pedro for the mainland.

Alex was expected to weaken as it passes over the Yucatan Peninsula, but forecasters say it will regain strength once it emerges Sunday afternoon over the warmer waters in the Gulf of Mexico.

The U.S. Hurricane Center in Miami said Sunday the storm had weakened to a tropical depression but expected it to become a tropical storm again by Monday.

Heavy rains are also expected to continue lashing southern Mexico and Guatemala until then.

The downpours have already proven deadly in northwestern Guatemala, where a landslide dislodged a rock outcrop, killing two men who had taken shelter underneath.

And in El Salvador, the national civil protection agency said two people are presumed dead after being swept away by rising rivers that broke their banks.

In Belize, where Alex first made landfall overnight Saturday, officials are relieved the country seems to have been spared major damage, but continue to monitor river levels.

Belize officials opened storm shelters in the island tourist resort of San Pedro late Saturday, as 1,400 people fled for the mainland by plane and by boat.

Tourists along Mexico's Caribbean coast were also warned to stay out of the rough surf kicked up by the storm, but as the storm passed there were no immediate reports of damage to the country's resort-studded coastline.

Besides the danger to people in its path, Alex is the first storm of the hurricane season to threaten containment efforts directed at the oil spill. An estimated 500 million litres of crude have spilled into the waters.

Should the storm take an unexpected sharp shift, there are fears it could seriously disrupt cleanup efforts in the Gulf.

The U.S. Coast Guard requires about five days for them remove the flotilla of boats and cleanup equipment from the Deepwater Horizon site, about 80 km off the coast of Louisiana, so they are keeping a close eye on reports from hurricane trackers.

"We all know the weather is unpredictable and we could have a sudden, last-minute change," Coast Guard Adm. Thad Allen said Saturday.

A tropical storm could also damage hundreds of kilometres of boom which has been put in place to contain some of the oil.

A number of attempts have been made to halt the flow of oil from the well that exploded on April 20, from installing caps to trying to plug the well with garbage, but have so far crews have been unable to completely halt the flow.