(Reuters) - "Bond King" Bill Gross, co-chief investment officer of PIMCO, butted heads on Thursday with billionaire investor Carl Icahn, telling Icahn to leave Apple Inc alone after he again urged the iPhone maker to initiate a tender offer to buy back $150 billion of its shares.
Icahn, meanwhile, revealed in a letter to Apple Chief Executive Tim Cook, made public on Thursday, that he had increased his stake by about 22 percent to just over 4.7 million shares since dining privately with Cook in September - underscoring his belief that the stock is undervalued.
Later on Thursday, he told CNBC that he is considering a proxy fight with Apple if the company rejects his proposal, which calls for the company to purchase the shares at $525 each. He added that he does not personally want a seat on Apple's board at this time.
Apple's shares ended regular trading on Thursday at $531.91, up 1.3 percent.
The activist investor, one of the best known managers in the $2.25 trillion hedge fund industry, said he would "test the waters" with other shareholders and "judge at that time" whether to pursue a proxy battle.
Icahn's demand for the $150 billion buyback, repeated several times publicly and privately to Apple's Cook since August, spurred a caustic Twitter comment from Gross: "Icahn should leave Apple alone & spend more time like Bill Gates. If Icahn's so smart, use it to help people not yourself."
In response, Icahn told CNBC that Gross is entitled to his own opinion.
"This is the business that he is in," said Colin Gillis, technology analyst at BGC Financial, referring to Icahn's latest move. "Whether that is in the best interest of Apple long-term remains to be seen."
Gillis, however, said Apple does have significant, unused cash that should be spent either on operations and investment or returned to shareholders.
"If you can't find a reason to deploy it then return it," he added.
Apple declined to comment.
In a public letter dated Oct 23 but published on Icahn's new investor-focused website on Thursday, the famously outspoken activist repeated calls for deep-pocketed Apple to use surplus cash to buy back shares. He said a $150 billion move could ratchet shares to an all-time high of $1,250 over three years.
"Irrational undervaluation as dramatic as this is often a short-term anomaly. The timing for a larger buyback is still ripe, but the opportunity will not last forever," Icahn warned in his letter, issued alongside the launch of his new website, "Shareholders' Square Table."
"While the board's actions to date ... may seem like a large buyback, it is simply not large enough given that Apple currently holds $147 billion of cash on its balance sheet, and that it will generate $51 billion" of earnings before interest and taxes, based on Wall Street estimates.
Icahn in August jump-started discussion about the pace at which Apple is returning cash to shareholders, when he tweeted he had taken a substantial position in the company. He has since kept Twitter followers informed of efforts to meet with Cook.
He is expecting to talk to Cook again, some time after Apple reports its financial results on Monday.
Mark Porterfield, a spokesman for Pimco, or Pacific Investment Management Co, confirmed the Twitter message was posted by Gross on the firm's Twitter stream, @PIMCO.
Read Icahn's letter at link.reuters.com/qak24v .
Icahn's new website, the launch of which was plagued with early glitches that barred access, seemed intended to further his goal of attacking underperforming corporate boards. It carries a quote from Icahn himself on the home page, from Texaco's 1988 annual meeting: "A lot of people died fighting tyranny. The least I can do is vote against it."
Analysts have said Icahn's newfound interest in Apple is helping improve sentiment on the stock. Icahn had argued as early as August that it could be worth $700 with a larger stock buyback program.
The company this week announced a new line-up of iPads for the holidays, along with plans to offer Mac users free operating and work software for life.
Icahn's latest proposal for Apple outlines a tender offer in which he himself will not participate.
In a tender offer, a company offers to purchase some or all of its investors' shares. Though tender offers usually come at a premium to the current share price, Icahn wants Apple to borrow money to make its offer at $525 per share, or about $7 less than the stock's closing price on Thursday.
In the letter, Icahn revealed he now owns 4.73 million shares of Apple stock, up from a previous total of 4 million. That means he owns nearly $2.5 billion worth of shares of the iPhone maker.
Apple is already in the process of spending $100 billion through 2015 on share buybacks, as well as dividend payouts. But Icahn says Apple should increase its share buyback program by the additional $150 billion.
"Per my investment thesis, commencing this buyback immediately would ultimately result in further stock appreciation of 140 percent for the shareholders who choose not to sell into the proposed tender offer," Icahn said.
"Furthermore, to invalidate any possible criticism that I would not stand by this thesis in terms of its long term benefit to shareholders, I hereby agree to withhold my shares from the proposed $150 billion tender offer," Icahn said. "There is nothing short term about my intentions here."
Additional reporting by Katya Wachtel in New York and Soham Chatterjee in Bangalore; Editing by Edwin Chan, Bernadette Baum and Andrew Hay