The surprise revelation from the billionaire activist caused a stir on Wall Street and pushed Apple's stock almost 5 percent higher to close at a 7-month high of $489.57 on the Nasdaq on Tuesday. Icahn said on Twitter that he had a "nice conversation" with Cook on Tuesday and they planned to speak again soon. Apple confirmed the conversation took place, but did not say if it influenced management's view of buybacks. Icahn told Reuters that the iPhone, iPad and Mac computer maker has the ability to do a $150 billion buyback now by borrowing funds at 3 percent. "If Apple does this now and earnings increase at only 10 percent, the stock - even keeping the same multiple currently - should trade at $700 a share," Icahn said in a phone interview. Apple has "huge borrowing power, little relative debt and trades at a low multiple." Icahn, who this year launched an assault on Michael Dell's $25 billion effort to take Dell Inc private, did not say how many shares of Apple he holds. A source familiar with the matter, who declined to be named because Icahn hasn't disclosed his holdings in Apple, said the investor's stake was worth around $1 billion, a fraction of the company's market value of more than $400 billion. U.S. rules require investors to disclose stakes of 5 percent or larger within 10 days of hitting that threshold. In April, Apple bowed to Wall Street pressure and said it would return $100 billion to shareholders by the end of 2015 - double the amount set aside previously. It got there in part by raising its dividend 15 percent and boosting its share buyback program six-fold to $60 billion, one of the largest of its kind.
The news gave Apple shares a lift, but they remain down more than 30 percent since hitting a record high of $702.10 in September 2012, pummeled by fears of slowing growth and thinning margins amid competition from Samsung Electronics.
"We currently have a large position in Apple. We believe the company to be extremely undervalued," Icahn said in one of two tweets about Apple on Tuesday.
"Had a nice conversation with Tim Cook today. Discussed my opinion that a larger buyback should be done now. We plan to speak again shortly," he said in his second tweet.
Icahn is the second prominent activist to target Apple this year. The company had averted a dispute with hedge fund manager David Einhorn of Greenlight Capital, who sued Apple to try to block a proposal regarding voting on preferred shares.
Apple eventually withdrew the proposal. Einhorn's $8 billion hedge fund is a major shareholder and owned about 2.4 million shares of the company as of the end of the first quarter.
"We appreciate the interest and investment of all our shareholders," Apple said in a statement on Tuesday in response to Icahn's tweets. "Tim had a very positive conversation with Mr. Icahn today."
Analysts said Icahn's interest in Apple helped cement improving sentiment on the stock, as investors began to anticipate a new line-up of gadgets in the fall, including possibly a cheaper iPhone that can spearheard a deeper drive into fast-growing emerging markets.
Speculation has persisted also that the company may be planning some sort of TV or smartwatch product - worn on the user's wrist - in the near future.
Cook said last month there will be products "in new categories" but gave no details.
Apple bought about more than $16 billion worth of stock in the June quarter, much more than analysts had expected.
"It's a heavyweight investor who can maybe accelerate the (buyback) program," said Morningstar analyst Brian Collelo. "It helps the positive momentum that Apple has seen."
Others say they saw little need for Apple to expand or speed up its buyback program. Much of the company's $147 billion in cash is held overseas, and that cash cannot be accessed without incurring taxes. As an alternative, Apple raised debt to bankroll its buyback program.
"It was already greatly increased and there was a debt offering to facilitate that," Hudson Square Research analyst Daniel Ernst said. "I can't say that I agree that the pace of the buyback is tepid."
Investors' biggest long-term concern about Apple is whether the company has lost its innovative edge. "Product innovation and profitability" are now top priorities, Ernst said.
Apple's profit fell 22 percent in the June quarter as gross margins slid below 37 percent from over 42 percent a year earlier.
On Tuesday, about 31 million Apple shares changed hands, almost three times the recent daily average. The stock is now up nearly $20 from its 200-day moving average of around $470.
Options volume was running three times the average daily turnover with 764,000 calls and 344,000 puts changing hands, according to options analytics firm Trade Alert.
Apple's options volume also accounted for 11.6 percent of the total single-stock options volume for the day, data from Trade Alert showed.