The footage, posted on wildlife site Latest Sightings (www.Latestsightings.Com), showed the unidentified man charging towards the startled animal.
With friends cheering and encouraging him, the man runs towards the elephant, falls to the ground but gets up again and bolts in the direction of the animal.
"Run at him right now, run," a voice of a fellow tourist is heard over the footage, which appeared to have been filmed by his colleagues.
The elephant initially swings its trunk towards the man, but soon makes its escape.
Latest Sightings said on its Facebook page that it received the video at the weekend but it was unclear when the incident occurred.
Wild animals in the two-million-hectare park sometimes attack visitors and elephants have been known to overturn the cars of sightseers.
The park's officials were not immediately reachable for comment, although wildlife advocates called for charges to be levelled against the tourist.
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