Human rights groups called on Swank, Jean-Claude Van Damme, violinist Vanessa-Mae and other celebrities to donate any money they received for socialising with the Chechen leader, who has been accused of committing atrocities.
Swank responded to the criticism by saying she had no idea about Kadyrov's alleged human rights abuses.
"I deeply regret attending this event. If I had a full understanding of what this event was apparently intended to be, I would never have gone," the Oscar winner said in a statement to The AP.
Van Damme and Vanessa-Mae have offered no comment so far.
Shakira was also rumoured to be attending Kadyrov's birthday party, but flatly denied she'd appear days before the event took place.
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Watch clips of Hilary Swank and Jean-Claude Van Damme at Ramzan Kadyrov's birthday party below: