Fire department commander Cleyton Bezerra said 10 people were missing, though it was unclear if they were under the rubble or just unreachable by relatives and friends. Ten survivors have been found along with an unidentified body.
"It is a difficult situation; there are parts (of the building) that can still collapse," said Bezerra, who led the rescue operation.
Authorities in the city of 2.6 million inhabitants in Brazil's northeast said two trapped people were communicating with relatives and rescuers by phone. Rescuers urged people at the site to be silent to allow them to hear noises in the rubble.
"For now we are trying to hear sounds that indicate where people are. There are several layers of debris," said fire department spokesman Romario Fernandes. He said the rescue operation is expected to last days.
Witnesses said they saw people in the building shortly before it collapsed.
Daiane Moreira was working next to the building when it collapsed.
"I just heard a boom and the building came down at once. A man came out drenched in blood and with a broken arm; he was the only one we could help," Moreira told journalists at the scene, as relatives and friends of building residents wept and waited for information.
Francineudo Rodrigues criticized the maintenance of the building where his father Francisco has worked as a doorman for eight years.
"I've seen cracks in columns; I've seen many problems that were not solved since I started coming here," Rodrigues told journalists.
Rodrigues, who also does jobs at the building, said his father is alive at a local hospital.
"Nothing ever changed in this building. It is the same as what I saw when my father started working here," he said.
Fortaleza Mayor Roberto Claudio said it was not immediately clear what caused the building to collapse. He promised a "rigorous investigation."
Andre Montenegro, the head of construction industry chamber in the state of Ceara, believes Tuesday's collapse happened "in a 30-year-old building that was clearly having problems with its maintenance, with its foundations."
Montenegro also said the crisis in Brazil's economy is preventing many owners of old buildings from investing in their renovation.
"A lot of investments in maintenance are being postponed for a later date, and sometimes that later date comes too late," he said.
The building is located in central Fortaleza about 2 miles (3 kilometers) south of the Iracema beach, one of the city's top tourist spots.
Tuesday's incident adds to a recent list of buildings collapsing in Brazil.
Another building partially gave way in Fortaleza in June. No one was injured, but the incident forced 16 families to move out.
In April a two four-story buildings collapsed in Rio de Janeiro, killing 24 people. The accident took place in a hillside area that was hard hit by rains and flash floods.
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