The reports said the highly experienced Kovats apparently died from a head injury after crashing into a cliff side. His 700-meter (2,290-foot) jump Tuesday afternoon was part of preparations for the Second World Wingsuit Championship being held in the park from Oct. 11 to 13.
The accident's cause wasn't immediately known, although the official Xinhua News Agency cited organizers as saying it may have been related to equipment failure or gusting winds. A video of the jump showed Kovats gliding toward a targeted landing spot before suddenly veering off course and disappearing into tree cover without deploying his parachute.
The World Wingsuit League expressed its condolences and said it was reviewing events leading up to Kovats' death and would adopt appropriate changes in the future.
"For the last three years we have worked closely on safety issues with the athletes, manufacturers and other experts. Still, when the world's best compete at the highest level in any sport, the risks remain," the league said on its website.
It said Kovats had been a three-time Hungarian national wingsuit champion.
Tianmen is in the Zhangjiajie scenic area that inspired the landscape in the Hollywood blockbuster "Avatar."