(CNN) Rescuers resumed searching Monday for a worker trapped in rubble after a deadly construction collapse in New Orleans, officials said, but the building's instability remains a dangerous situation.

"It is still a very, very dangerous building, a dangerous situation," New Orleans Fire Department Superintendent Tim McConnell said Monday. "That tower is still heavily damaged and unsecured, and we're a long way from being in a safe mode."

As engineers worked to stabilize the building, search dogs went through the site searching for the missing worker, McConnell said. They entered the building five times Monday, McConnell said.

Two people were killed in Saturday's collapse and at least 30 people were hospitalized, authorities said. All but one of the injured have been discharged, they said.

The Orleans Parish Coroner's office on Monday identified one of the dead as Anthony Floyd Magrette, 49. Crews were still working to remove the second body, Mayor LaToya Cantrell told reporters Sunday evening.

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