Families have been frantically trying to help rescue workers pick their way through the flattened three-storey building, in which at least 21 youngsters and four adults died.
A crowd of parents waiting outside claimed two families have received WhatsApp messages from two trapped girls.
The newspaper El Universal reported that one trapped girl, Fatima, sent a WhatsApp message to her relatives saying: “I’m fine, I’m with four other trapped children, help us, we’re thirsty.”
It is not known if Fatima is among the 30 or so children who have been rescued so far from the Enrique Rebsamen School, which like dozens of other buildings in Mexico City has been turned to rubble.
Up to 30 youngsters and eight adults were initially declared missing in addition to those who were known to have died.
TV pictures showed rescue teams working in the dark, using picks, shovels and their hands as well as heavy lifting gear in an attempt to find survivors.
One boy who was pulled out alive by a soldier, named Victor by El Universal, said he was thirsty but could barely breathe after being crushed by a fence.
A volunteer rescue worker, 29-year-old doctor Pedro Serrano, crawled through a crevice in the debris and made it into a classroom.
He found the bodies of three more people – two adults and a child – which he was unable to remove because it was too dangerous.
He said: “We dug holes, then crawled in on our bellies. We managed to get into a collapsed classroom. We saw some chairs and wooden tables.
“The next thing we saw was a leg, and then we started to move rubble and we found a girl and two adults a woman and a man.”
Anxious relatives have described their fears as they grow increasingly concerned.
“They keep pulling kids out, but we know nothing of my daughter,” said 32-year-old Adriana D’Fargo, whose seven-year-old was missing.
The doctor said he had not given up hope of finding more children alive.
“We can hear small noises,” he said.
“We don’t know if they’re coming from above or below – from the walls above, or from someone below calling for help.”
Occasionally, the volunteers and emergency personnel at the school have been asking for silence so they can listen for signs of life.
Silently, as they continue to work way into the night, they hold their fists in the air in a gesture of hope and solidarity.