Sean Parker, Facebook's first company president, rejected one analyst's claims that Facebook would "disappear in five to eight years."

Erik Jackson, founder of Ironfire Capital, told CNBC Monday on Squawk on the Streetthat in less than a decade Facebook would lose its prominence in the web realm.

"In five to eight years they are going to disappear in the way that Yahoo has disappeared," Jackson said.

Parker, however, spoke to CNBC on Tuesday after the launch of his new start-up Airtime, a social video app, and said the demise of Facebook is unlikely.

"Analysts have been predicting the demise of Facebook since the very early days. There were these predecessors, like Friendster and MySpace that basically seemed like fads, but failed for reasons that had nothing to do with culture. They had to do with technology," Parker said. "Facebook is such a basic utility. It's something that is such a part of peoples' lives, I think it's hard to imagine it going away."

Facebook stock is down almost 28 percent from its IPO price of $38 and dipped below $26 to 25.88 for the first time Tuesday. Despite the lower share price, Parker said he has been relieved since the social network's market debut.

"There was almost a sense of relief with the IPO. There was such a speculative market around Facebook shares, in particular the retail investor. I think that's no longer an issue for the company. That's probably a good thing," Parker said. "Eventually, you want the stock to stabilize and you basically want to have a lot of large institutions who take a long view."