(Updates body count, adds bad weather alert)

By Jose Cortes

ELOXOCHITLAN, Mexico, July 5 (Reuters) - Mexican rescuers dug out the bodies of 31 people on Thursday and searched for dozens more believed killed when part of a rain-soaked mountain collapsed on a bus carrying up to 60 passengers.

About 500 soldiers and rescue workers labored with pick-axes and shovels and used dogs to find the victims, hit by the mudslide on a remote road near the mountain town of Eloxochitlan in the southern state of Puebla.

Rescuers also used bulldozers and other heavy machinery to claw away boulders, dirt and trees to reach the bus, which was buried under some 23 feet (7 meters) of mud after the hillside collapsed early on Wednesday.

"We don't expect to find anyone alive," local government spokesman Javier Lopez said in the state capital Puebla.

The corpses of at least four children were pulled out as emergency workers dug up crumpled chunks of the bus, which was crushed on a winding road about a mile (1.6 km) below the tiny village of Zacacuapan.

Villagers heard the landslide but only realized what had happened when the bus failed to arrive.

"We got down there and it was all covered up and we realized something had happened because the bus never arrived," said coffee grower Benito Cortes, 30, who said he knew most of the victims.

Rescuers were hampered on Thursday by the flattened condition of the bus and concerns that more of the sodden hillside could give way.

"The part of the bus they are working on is completely destroyed," Puebla Gov. Mario Marin told Mexican radio, adding that rescue workers would keep digging until they reached the last body.

The start of the rainy season in Mexico has brought driving rain to many parts of the country, saturating hillsides that are home to poor farming communities.

The Eloxochitlan area is one of the poorest regions in Mexico.

It had endured heavy rains in recent days and is prone to small landslides but the scale of Wednesday's disaster stirred memories of mudslide disasters in southern Mexico and Central America after the rains of Hurricane Stan in 2005.

Emergency services said more heavy rain was likely and warned locals to be on alert for floods and swollen rivers.

It took rescue teams hours to reach the scene of the accident on Wednesday from nearby cities.

Relatives of missing people waited through the night at the scene of the accident and held candlelight vigils.

"A lot of them were teachers. They were my friends," a local man who saw the mudslide happen told Mexican television. (Additional reporting by Anahi Rama and Catherine Bremer in Mexico City)

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