Dallas police Sgt. Gil Cerda told The Dallas Morning News that a crane operator was raising a hook when the cable snapped and the hook fell on the worker.
Kevin Messenger, chief operating officer for Lewis Equipment Co., said in a statement there "are more questions than answers" about what happened.
"We are deeply saddened about the loss of life," Messenger said.
The name of the worker was not immediately released because the family had not been notified as of Wednesday evening, said Matt Papenfus, general manager of Turner Construction.
The employee did not work for Turner but for a subcontractor called TXI, Papenfus said. TXI did not immediately return a phone message Wednesday.
Federal safety officials will help investigate the cause of the accident on Thursday. Work at the site, which will be a high-rise condominium complex, is on hold until the investigation is complete.
"We are cooperating fully with the investigations," Papenfus told The Associated Press. "Operations will not continue until that inspection shows that everything is OK."
Papenfus said Turner has one other construction site in Dallas involving a crane, and that crane was inspected Tuesday.
In late March and early April, city building officials took an inventory of cranes being used in Dallas after seven people were killed when a crane collapsed in New York. That inventory listed two cranes used at the site of Wednesday's accident as being new, according to city documents obtained by The Associated Press.
Information about the cranes was given to city officials by a project superintendent, according to the documents. Lewis Crane performed the inspections, which were recorded as current. Crane operators on the site were certified, the inventory said.
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