The prank should be filmed and uploaded to Battlecam - a site where people can upload videos and which also serves as a community hub for David's TV on demand Web site FilmOn.
The company later clarified that the video should be streamed live, as content on Battlecam is broadcast live.
"Most people in the community thought the $100,000 wasn't enough for the audacity of the dare," David told CNBC.com. "One million is a nice, round number and that gets people's attention a lot more."
Costs such as lawyers and fines needed to be taken into account, said David, who added that he was contacted by between 150 and 160 "serious" applicants for the prank.
"I really would like to see the challenge happen," he said. "I think somebody will genuinely do it or try doing it."
If it happens, the prank would ensure publicity for Battlecam but also "I think it's important to understand that I have been doing pranks all my life," David said.
Asked why he chose Obama as the victim, the billionaire explained that it is because of the US President's global reach.
"I have nothing against him, I think he's an awesome human being, I really do. He just happens to be the wrong president at the wrong time," he said.
Even the British Queen is "not big enough" to give a global audience to such a prank, David said, but added: "ok, why not, let's do one on the Queen as well, but keeping it in perspective I think I'd put a price tag of, I don't know, $200,000 on the Queen."
He said his most outrageous prank was taking six people across Europe under the pretext of doing a music video with twin Romanian-born singers Cheeky Girls. The six were arrested and interrogated for the murder of the Cheeky Girls on a Greek island.
"Fame is an incredible narcotic," David said. "The TV cameras seem to have an amazing effect on how people will behave."