Three buildings collapsed in the historic center of Rio de Janeiro, Brazil, on Wednesday January 25, 2012, sending rubble and dust flying through the air.

Sao Paulo (CNN) — The death toll in the collapse of three buildings in Rio de Janeiro rose to 13 on Friday as rescuers said they held out little or no hope of finding more survivors, state media reported.

A woman’s body was discovered Friday in the rubble, said Col. Sergio Simoes, secretary of civil defense, according to the state-run Agencia Brasil news agency.

One survivor was located Wednesday night. The city’s fire department has said 20 people were missing, but it was not clear if that number had dropped because of the discovery of more bodies.

“Although the culture of the fire department is driven by hope, motivation, given the scenario that we’re checking, and time passed since the accident, I must say that we do not work with the possibility of more survivors,” said Simoes, according to Agencia Brasil.

Simoes, who also serves as fire brigade commander, said he was concerned about large chunks of concrete possibly falling on crews.

Rescue efforts may be completed by Sunday.

It was not immediately clear what caused the collapse of a 20-story building and adjacent 10- and 4-story buildings on Wednesday night. Officials said they were investigating both the possibility of a gas leak and a structural failure.

Sergio Cabral, the governor of Rio de Janeiro state, declared three days of mourning for the victims.

Among those who died in the collapse was Cornelio Ribeiro Lopes, 73, who was the doorman for one of the buildings, Agencia Brasil reported. He lived there with his wife, Margarida Vieira de Carvalho, who is among the missing, the agency reported.

Rescuers said that one of the biggest challenges in finding people was the dust cloud that floats in the area.

The accident came at a delicate time for Rio de Janeiro as the city prepares to host the World Cup in 2014 and the Olympic Games two years later.