OAXACA, Mexico-- Rescue efforts resumed Wednesday for 11 people missing after a huge hillside collapsed on a town in Mexico's rain-soaked southern state of Oaxaca, while a landslide in a neighboring state killed a dozen people.

The government delivered blankets and other supplies to survivors and other who fled their unstable homes for fear of more mudslides in Santa Maria de Tlahuitoltepec. Many sheltered under makeshift tents on the hills.

The landslide early Tuesday caused nationwide alarm after local authorities initially said hundreds could be dead in the remote town, which had been blocked off by slides and a washed-out bridge.

But hours later, when rescue workers finally reached the community, only 11 people were missing and none confirmed dead.

Heavy rains are beleaguring much of Mexico's south. In neighboring Chiapas state, at least 12 people were killed Wednesday by a landslide in the municipality of Amatan.

"Unfortunately there has been a new landslide in Amatan, Chiapas. We are mobilizing aid to help. The governor informed me of 12 deaths," President Felipe Calderon said by Twitter.

The chief of the Chiapas state Civil Protection emergency response agency, Salvador Cervantes, confirmed the death toll and said the victims were buried when earth slid down a hill onto their homes.

In the Oaxaca slide, rains and unstable soil forced police and firefighters to suspend the rescue efforts for hours. The search resumed Wednesday with picks, shovels and a bulldozer in the river of mud and stones that swept down the hillside. No bodies had been recovered by the afternoon.

Among the missing were the town's chief health official, his pregnant wife and their two teenage daughters, Mayor Antonio Martinez said.

The area was battered by the remnants of a hurricane one week and a tropical storm the next.

Oaxaca Gov. Ulises Ruiz initially told a Mexico City television station he had received reports that 300 homes were buried, with as many as 1,000 people inside.

But the estimates of casualties were gradually lowered during the day, and Tuesday night the governor confirmed that only 11 people were missing. Martinez said 10 houses were buried.

As they waited for police and firefighters, residents used backhoes and other rudimentary tools to find their neighbors Tuesday, but made little progress. They said most of the homes were completely covered and no voices could be heard within.

The U.S. government offered to pay for a team of Mexican rescuers to travel to the site.

Oaxaca state's Civil Protection operations coordinator, Luis Marin, said the state had seen three days straight of intense rain. The state government warned residents south of the city of Oaxaca of flooding from overflowing rivers and opened shelters in other parts of the state.

Santa Maria de Tlahuitoltepec, which had 9,000 residents in 2005 according to Mexican census data, is a community high in the Sierra Norte mountains known for maintaining its indigenous culture, especially its music. Residents speak the native language, Mixe, and its youth orchestra plays throughout Mexico.