VILLAHERMOSA, Mexico — Hungry and dehydrated victims of one of the worst floods in Mexico’s history scrambled for government packages of food and medicine, while at least 20,000 people remained trapped yesterday on the rooftops of homes swallowed by water.

Residents were running dangerously short of food and water after nearly a week of floods left 80% of the Gulf Coast state of Tabasco under water and destroyed or damaged the homes of about half a million people. Governor Andres Granier ordered central streets in the state capital of Villahermosa closed to all but rescue workers. Authorities said two more bodies were found Sunday in the brackish waters covering much of the region. If the deaths are confirmed to have been caused by the flooding, the disaster’s death toll would stand at 10. Government officials worked furiously to distribute aid, and authorities continued trolling the water-filled streets looking for stranded residents.

Villahermosa, the state capital, was still completely under water, though river levels had begun to drop after rising to historic levels. The National Water Commission said it had begun efforts to start pumping the streets.

Desperation grew among residents who could not get their hands on government-supplied food and water or who found themselves cut off from crucial medical supplies. Garbage piled up in the murky waters days after the city suspended most public services including trash collection.

As helicopters carrying aid made stops in hard-hit areas, disputes broke out among victims who pushed through crowds and struggled frantically for the packages. “People are fighting over food and water, and the lack of electricity and running water are making life in the city impossible,” said Martha Lilia Lopez, who has been handing out food on behalf of a nonprofit foundation she heads. Daniel Montiel Ortiz, who oversaw helicopter rescue efforts for the federal police, said rescuers were now focused on “selective evacuations” — primarily of sick people — and delivering badly needed supplies to isolated communities still surrounded by water. Some people broke into shuttered stores and took food and household goods, and police reported detaining about 50 people for looting over the last couple of days. But Mr. Ortiz called those “isolated incidents.”

Soldiers created makeshift docks out of sandbags for boats that trolled the water-filled streets, rescuing stranded victims. Some people hitched boat rides back to homes they abandoned a week earlier to retrieve medication, clothing, and other supplies before returning to shelters.