Activist investor Carl Icahn disclosed Thursday he has raised his stake in Apple, and urged an "immediate" buyback of shares to boost the stock price of the US tech giant.

Icahn, in a letter to Apple chief executive Tim Cook, said he now has some $2.5 billion worth of Apple stock and "we currently intend to buy more."

Based on Apple's current value, Icahn's stake of 4.73 million shares is worth around half of one percent of the market value of the maker of iPhones and iPads.

But the billionaire corporate raider said Apple can boost its sagging share price by purchasing $150 billion in shares, using some of its available cash and borrowing for the rest.

"If the company decided to borrow the full $150 billion at a 3 percent interest rate ... the result would be an immediate 33 percent boost to earnings per share, translating into a 33 percent increase in the value of the shares," he said in the letter.

"Longer term (in three years) if you execute this buyback as proposed, we expect the share price to appreciate to $1,250," assuming adjusted profit growth of 7.5 percent annually.

Apple shares, which hit a record above $700 last year, were flat at $525.02 in early trade. The stock has been hit by concerns that Apple is losing its edge in innovation along with market share in the key smartphone and tablet markets.

Icahn said he was "supportive" of Cook but added that "per my investment thesis, commencing this buyback immediately would ultimately result in further stock appreciation of 140 percent."

He said he would hold his shares in the event of a buyback because "there is nothing short term about my intentions here."

Icahn released the letter as he launched a new website called Shareholders' Square Table, dedicated to "fighting tyranny" of corporate boards and CEOs and defending shareholder rights.

Icahn met Cook over dinner on September 30 for discussions on the buyback, which Icahn has talked about over several weeks.

Earlier this year, Apple yielded to pressure from the hedge fund Greenlight Capital, agreeing to return some $100 billion to shareholders over the next two years, including $60 billion in share repurchases.

Icahn has a long history of taking positions in companies that give him the leverage to force changes in management or provide dividends to shareholders.

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APPLE INC