Bender's comments come a day after Thurman blasted him, along with disgraced Hollywood producer Harvey Weinstein and E Bennett Walsh, for allegedly covering up the incident.
"I deeply regret that Uma suffered the pain she has, both physically and emotionally, for all of these years from the accident that occurred on the set of 'Kill Bill'," Bender said Wednesday in a statement, according to Entertainment Weekly.
"The safety of the professionals who work on the movies I produce is vital to me and I never want to let anyone down," he added.
"I never hid anything from Uma or anyone else nor did I participate in any cover up of any kind and I never would," he said.
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Thurman had recently released the dramatic on-set video showing her driving a convertible and careening into a tree.
The actor had clarified that director Quentin Tarantino had nothing to do with the alleged cover up.
"Tarantino was deeply regretful and remains remorseful about this sorry event, and gave me the footage years later so I could expose it and let it see the light of day, regardless of it most likely being an event for which justice will never be possible," she wrote on her Instagram page.
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