Eduardo Verdugo, Associated Press
People evacuate a flooded area in Villahermosa, Mexico, Saturday. Many victims have spent the better part of a week trapped by the rising waters, and authorities warned of a possible health crisis and scattered reports of looting as supplies run out.

VILLAHERMOSA, Mexico — The death toll in the widespread flooding in southern Mexico rose to eight on Saturday as rescuers struggled to evacuate people from rooftops and bring supplies to those protecting their homes from would-be looters.

The department of civil defense in Chiapas state, which borders on Guatemala, reported finding seven bodies between Friday and Saturday. The dead included five adults swept away by swollen rivers, a 25-year-old undocumented Honduran immigrant who drowned while trying to cross a river, and an 8-year-old girl who fell from a bridge.

In the neighboring Tabasco — where one man died earlier in the week, and where almost 80 percent of the state was covered in water — the level of some rivers began to recede slightly Saturday. The government also said it would reduce water outflows from a dam upstream.

Still, the state capital of Villahermosa remained largely flooded and prey to horrifying rumors — that crocodiles, which normally live along the banks of some rivers, had invaded the murky floodwaters in the city's center, or that the dam upstream was about to burst.

The Tabasco state government said the dam was not in danger but had no immediate comment on the crocodile rumor. Officials instead concentrated on supplying food and water to tens of thousands of people at emergency shelters, and others who had decided to ride out the flood on the roofs of their homes, in a bid to discourage looters.

Many victims have spent the better part of a week trapped by the floodwaters, and authorities warned of a possible health crisis. President Felipe Calderon, who surveyed the zone from the air Friday, called the flooding one of Mexico's worst recent natural disasters.

Calderon ordered the armed forces and federal police to maintain order and prevent looting, but local radio reported that desperate residents had begun sacking markets for supplies.

Emergency shelters already held 69,000 flood victims, but tens of thousands more were leaving the state entirely, as food, water and power became increasingly scarce.

"We are not going to fight over food. Everybody here has suffered the same," said Maria del Carmen Arias, 48, as her granddaughter slept in her lap at an improvised shelter at a Villahermosa church. Arias said her family may leave the city as well, to stay at a relative's farm.

Tons of supplies and medical aid streamed into the region aboard planes and trucks, but little food and water was available in stories in Villahermosa, where intermittent rains fell early Saturday.

Some roads were cut off by floodwaters, making it hard to distribute supplies. Elsewhere, highways were clogged with flood victims camped out on roadbeds — the highest terrain available in some rural areas.

A week of heavy rains caused rivers to overflow, submerging at least 80 percent of the oil-rich state.