In a CNBC interview Icahn called Apple a "no brainer."
"The point is that you don't have to be genius in technology to understand that Apple is selling at a 2014 consensus of 9 times earnings, and amazingly the S&P is selling at 17 times earnings and Apple is really growing," Icahn said in a "Fast Money Halftime Report" interview.
He added that in some ways, he was better off if the company did not increase its buyback, because the stock would remain cheap enough by his standards to buy more.
While Icahn also said he was not criticizing management for the way it runs the company, he took issue with the board for what he called a lack of finance experience.
"What they're doing I think is ludicrous in not taking it up right now," Icahn said of the board's reticence to raise the company's ongoing share buyback.
Apple shares rose 1.3 percent in afternoon trade to $556, some $87 above where the stock was when Icahn started buying last year.
At one point in 2013 Icahn suggested Apple could buy back as much as $150 billion in stock, though he later tempered that push.
His $3 billion stake represents less than 1 percent of Apple's stock.
Separately, Icahn also said he was planning to unveil another major stake in a new company over the next few weeks, likely on Twitter.
But he declined to confirm reports that he has taken a stake in car rental company Hertz.
- By CNBC.com