Brussels - The European Union has offered its assistance to Mexico and expressed condolences to the victims of the earthquake, European Commission Spokesman Margaritis Schinas said.
"We are here if anything is needed," Schinas said.
European Commission President Jean-Claude Juncker has sent a letter offering help to Mexican President Enrique Pena Nieto.
"Our capabilities to provide urgent support have been put on alert, as our Emergency Response Coordination Centre is monitoring the situation on the ground," said EU foreign policy chief Federica Mogherini and European Commissioner for Crisis Management Christos Stylianides in a joint statement.
Firefighters, soldiers, police and volunteers were digging out the dead and searching for survivors in the rubble left by a powerful quake that struck central Mexico, killing more than 200 people and toppling multistory buildings.
Rescue operations were under way across the quake zone, including at a Mexico City school turned to ruins.
At least 32 children and five adults were killed after the Enrique Rebsamen school collapsed, local broadcaster Televisa reported. Eleven children have already been saved.
Death toll expected to rise
"We estimate that there are still 30 or 40 people trapped in the rubble," Mexican marines spokesman Jose Luis Vergara told Televisa. "We are hearing voices. Some are still alive."
According to Televisa, rescue services are in contact with a young boy named Victor, who is trapped beneath the rubble and being provided oxygen through a long tube.
A spokesman for the rescue services said that they are also in contact with a trapped teacher, who has a small girl by her side.
President Enrique Pena Nieto, who visited the school in the south of the capital during the night, spoke of the solidarity of the people in their response to the tragedy.
More than 700 people were injured, about 400 of them seriously, in the magnitude-7.1 quake on Tuesday. In addition to the capital, the central Mexican states of Morelos and Pueblos were also hard hit.
At least 226 people were killed, Interior Minister Miguel Angel Osorio Chong said, with the death toll expected to rise.
Several wrecked hospitals were forced to shut their doors and treat patients in the open air. The Education Ministry said 209 schools have been closed, 15 of them with severe damage.
Electricity was knocked out to 3.8 million people, power company CFE said, and the telephone network in the capital was erratic.
Mexico City's world-famous Azteca stadium - the scene of Diego Maradona's "hand of God" goal against England at the 1986 World Cup - was another casualty of the quake. Photographs circulated by local media showed a large crack in one of its stands.
Messages of support
The quake came as Mexico was still recovering from a deadly magnitude-8.1 tremor in the country's south less than two weeks ago and on the anniversary of a quake that hit in 1985, which killed an estimated 10,000 people.
Pope Francis, during his Wednesday weekly audience in St Peter's Square, called it a "time of sorrow."
"Let us all raise our prayers to God so that he may welcome into his bosom all who have lost their lives and comfort the wounded, their families and all those affected," he said.
Messages of support came pouring in from other world leaders, including Chancellor Angela Merkel, who pledged Germany's solidarity with Mexico in a letter to President Nieto in which she expressed her "sorrow and dismay."
"Be assured that Germany will stand by you," she wrote.