The massive crane, capable of lifting 1 million pounds, was owned by Deep South Crane & Rigging, which Saturday released the names of its four workers killed in the accident.
"We wish we had all of the answers on what happened and why - but we do not - and speculating on cause would not resolve anything," the company said in a statement. "But we are actively working to find those answers."
The four men killed were: Marion "Scooter" Hubert Odom III, 41, of Highlands; John D. Henry, 33, of Dayton; Daniel "DJ" Lee Johnson, 30, of Dayton; and Rocky Dale Strength, 30, of Santa Fe, Texas.
At the LyondellBasell refinery, company officials said they were trying to restore normalcy. The refinery brought in grief counselors and will hold a series of safety meetings to address concerns about the accident starting Monday, said David Roznowski, a company spokesman.
"This is a real blow to our refinery team, and it will take some time to recover from this," said Roznowski.
Investigators with the Occupational Safety and Health Administration began their formal accident investigation early Saturday, Roznowski said.
Cameras are mounted around the plant and refinery officials said the company hopes the video will help determine what happened.
Two of the injured workers remained in Houston hospitals Saturday. Their injuries were not life-threatening, Roznowski said.
Two other injured workers were taken to a hospital and have since been released. Three others were treated and released at the scene, fire officials said.
The first lawsuit stemming from the collapse was filed in Harris County state district court, the Houston Chronicle reported.
The lawsuit was filed on behalf of Grant Pasek, a worker injured after jumping from an elevated bucket when he saw the crane start to fall. It seeks a temporary restraining order to preserve the scene and evidence relating to the accident, attorney Jim S. Hart told the newspaper.
Pasek, a lineman, was working in a bucket about 45 feet in the air when he saw the crane start to fall, his attorney said.
The massive crane fell Friday afternoon with enough force to lift workers off the ground, and toppled across another smaller crane and a tent where workers were eating lunch.
Crane safety has been getting extra scrutiny in recent months because of an alarming number of crane-related deaths in places such as New York, Miami and Las Vegas.
The crane failed and collapsed during maintenance, LyondellBasell officials said. It had not been scheduled to do any work until next week, but was idling after it hit the ground, said Jim Roecker, the company's vice president for refining.
The maintenance project has been suspended for a week, but refinery operations at the plant were operating normally, said Roznowski. The refinery has about 3,000 employees and 1,600 contract workers.