VILLAHERMOSA, Mexico, Oct 31 (Reuters) - Thousands of homes were flooded on Wednesday after several rivers burst their banks in the southern Mexican state of Tabasco and heavy rains left 70 percent of the swampy region under water.

The Tabasco state government said 20,000 people were rushed to shelters after floodwater poured over sand-bagged riverbanks and into hundreds of villages and towns, including state capital Villahermosa.

The floods, caused by a cold front that has wreaked havoc with the oil industry along Mexico's Gulf coast, were the worst in the state's history, said Gov. Andres Granier.

"Water normally covers 34 percent of Tabasco's surface, but at the moment, I can assure you that more than 70 percent is water," Granier said.

Floodwater half-covered several giant carved stone heads built by the Olmecs, America's first great civilization, at the state's La Venta archeological site. Some of the heads are over 9 feet (3 meters) tall.

Tabasco is a low-lying and oil-rich state on Mexico's tropical Gulf coast. Much of the territory is covered by rain forests and mangrove swamps.

Bad weather from the cold front caused an oil platform to collide with another rig last week, killing at least 21 workers. Stormy seas closed Mexico's three main oil ports on Sunday, halting almost all exports and a fifth of production. Two of the ports were operating again on Wednesday.

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