A damaged car is seen outside a building after an earthquake in Mexico City, Mexico, Sept 19, 2017.[Photo/Agencies]

Dozens of buildings tumbled into mounds of rubble or were severely damaged in densely populated parts of Mexico City and nearby states. Mayor Miguel Angel Mancera said buildings fell at 44 places in the capital alone as high-rises across the city swayed sickeningly.

Hours after the magnitude 7.1 quake, rescue workers were still clawing through the wreckage of a primary school that partly collapsed in the city's south looking for any children who might be trapped. Some relatives said they had received Whatsapp message from two girls inside.

The federal Education Department reported late Tuesday night that 25 bodies had been recovered from the school's wreckage, all but four of them children. It was not clear whether the deaths were included in the overall death toll of 226 reported by the federal civil defense agency.

President Enrique Pena Nieto visited the school earlier in the night. At the time, he said 22 bodies had been found, and added in comments broadcast online by Financiero TV that 30 children and eight adults were reported missing. Rescuers were continuing their search and pausing to listen for voices from the rubble.

Later, Pena Nieto issued a video message urging calm and saying the initial focus of authorities is on finding people trapped in fallen buildings.

"The priority at this moment is to keep rescuing people who are still trapped and to give medical attention to the injured people," he said.

The quake is the deadliest in Mexico since a 1985 quake on the same date killed thousands. It came less than two weeks after another powerful quake caused 90 deaths in the country's south.

Luis Felipe Puente, head of the national Civil Defense agency, reported early Wednesday that the confirmed death toll had increased to 226.

His tweet said 117 dead had been counted in Mexico City and 55 in Morelos state, which is just south of the capital. It said 39 were known dead in Puebla state, where the quake was centered. Twelve deaths were listed in the State of Mexico, which surrounds Mexico City on three sides, and three in Guerrero state.

The federal government declared a state of disaster in Mexico City, freeing up emergency funds. President Enrique Pena Nieto said he had ordered all hospitals to open their doors to the injured.

Mancera, the Mexico City mayor, said 50 to 60 people were rescued alive by citizens and emergency workers in the capital. Authorities said at least 70 people in the capital had been hospitalized for injuries.

The federal interior minister, Miguel Angel Osorio Chong, said authorities had reports of people possibly still being trapped in collapsed buildings. He said search efforts were slow because of the fragility of rubble.

"It has to be done very carefully," he said. And "time is against us."At one site, reporters saw onlookers cheer as a woman was pulled from the rubble. Rescuers immediately called for silence so they could listen for others who might be trapped.