In a post on her Facebook page, Williams made her first public comments on the June 9 car crash in which police said she was "at fault".
"I am devastated and heartbroken by this accident," Williams wrote. "My heartfelt condolences go out to the family and friends of Jerome Barson and I continue to keep them in my thoughts and prayers."
Williams, 37, is a seven-time Grand Slam champion who won five Wimbledon titles from 2000 to 2008 plus the 2000 and 2001 US Opens.
Attorney Michael Steinger told ABC television Friday that Barson's family will file a wrongful death suit over the incident in Palm Beach Gardens, Florida.
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Barson, who suffered head injuries in the accident, died two weeks later on June 22.
A Palm Beach Gardens police report said Williams' 2010 Toyota Sequoia SUV and a 2016 Hyundai Accent driven by Barson's wife, Linda Barson, collided in an intersection.
The accident remains under investigation and Williams has not been charged.
"This is an unfortunate accident and Venus expresses her deepest condolences to the family who lost a loved one," he said.
Cunningham said Williams entered an intersection on a green light that turned red during her turn, but she was stuck in the intersection because of traffic.
The police report said Williams was deemed at fault for blocking the right of way of the other vehicle.
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