(Corrects quake depth to 51 km from 31 km in last paragraph)
By Daniel Trotta and Adriana Barrera
MEXICO CITY, Sept 21 (Reuters) - Rescuers labored against long odds into the dawn on Thursday to save a 12-year-old schoolgirl and untold other survivors who may be trapped beneath crumpled buildings in central Mexico following the country's deadliest earthquake in 32 years.
More than 50 survivors have been plucked from several disaster sites since Tuesday afternoon's 7.1-magnitude quake, leading to impassioned choruses of "Yes we can!" from the first responders, volunteers and spectators gathered around the ruins.
At least 237 others have died and 1,900 were injured.
As the odds of survival lengthened with each passing hour, officials vowed to continue with search-and-rescue efforts such as the one at a collapsed school in southern Mexico City where Navy-led rescuers could communicate with the 12-year-old girl but were still unable to dig her free.
Eleven other children were rescued from the Enrique Rebsamen School, where the students are aged roughly six to 15 but 21 students and four adults there were killed.
Rescuers previously had seen a hand protruding from the debris and the girl wiggled her fingers when asked if she was still alive, according to broadcaster Televisa, whose cameras and reporters had special access to the scene to provide nonstop live coverage.
But some 15 hours into the effort, Admiral Jose Luis Vergara said rescuers still could not pinpoint her location.
"There's a girl alive in there, we're pretty sure of that, but we still don't know how to get to her," Vergara told Televisa.
"The hours that have passed complicate the chances of finding alive or in good health the person who might be trapped," he said.
As Vergara spoke, a human chain of hard-hatted rescuers removed a large chunk of concrete from the floodlit scene.
Rescuers periodically demanded "total silence" from bystanders, who would freeze in place and stay quiet to better hear any calls for help.
As with other disaster sites throughout central Mexico, officials dared not employ heavy lifting equipment for fear of crushing anyone below.
Throughout the capital, crews were joined by volunteers and bystanders who used dogs, cameras, motion detectors and heat-seeking equipment to detect victims who may still be alive. Some 52 buildings collapsed in Mexico City alone and more in the surrounding states.
The quake killed 102 people in Mexico City and the remaining 135 from five surrounding states, officials said late on Wednesday.
At least nine Latin American countries pledged to rush in search-and-rescue teams or technical assistance, with crews from Panama and El Salvador already on the job, as did the United States, Spain, Japan and Israel.
The Panamanian team of 32 rescue workers dressed in orange jumpsuits and helmets and two dogs arrived with seven days' worth of food, water and supplies and prepared to work around the clock, said Cesar Lange, leader of the Panamanian Civil Protection unit.
The earthquake struck about 150 km (90 miles) southeast of Mexico City on Tuesday afternoon, shattering glass, shearing off sides of buildings and leaving others in dusty piles of destruction.
It came on the same date as a 1985 tremor that killed thousands and still resonates in Mexico. Annual September 19 earthquake drills were being held a few hours before the nation got rocked once again.
Mexico was still recovering from another powerful quake less than two weeks ago that killed nearly 100 people in the south of the country.
The epicenter was 51 km (32 miles) beneath the surface, sending major shockwaves through the metropolitan area of some 20 million people. Much of the capital is built upon an ancient lake bed that shakes like jelly during a quake.
Reporting by Daniel Trotta and Adriana Barrera; Editing by Matthew Mpoke Bigg