Icahn, who is in the midst of a fierce battle over computer maker Dell and has a history of taking stakes in firms to seek shakeups, announced his move yesterday on Twitter.
"We currently have a large position in APPLE," he tweeted. "We believe the company to be extremely undervalued. Spoke to (Apple chief executive) Tim Cook today. More to come."
In a second tweet moments later, Icahn said he would press Apple to increase its stock buyback, in which the company purchases its own shares in a bid to boost its value.
Apple shares, which had been flat most of the day, jumped on the news and closed up 4.75 per cent at USD 489.57.
Asked about the Icahn action, Apple spokesman Steve Dowling said in a statement: "We appreciate the interest and investment of all our shareholders. Tim had a very positive conversation with Mr. Icahn today."
Shares in Apple last year surged to a record above USD 700 but have been in a deep slump over concerns the maker of the iPhone and iPad has been losing its edge in innovation.
its steep decline in recent months.
Earlier this year, Apple yielded to pressure from the hedge fund Greenlight Capital, agreeing to return some USD 100 billion to shareholders over the next two years, including USD 60 billion in share repurchases.
Apple shares posted gains Monday after a report saying the California tech giant was set to announce its next iPhone at a September 10 event.
The Dow Jones news website AllThingsD reported Sunday that Apple scheduled an event next month where it will announce its newest iPhone in an effort to regain ground lost to Samsung and other smartphone makers, most of which use the Google Android operating system.
A recent IDC survey showed Apple's share of the global smartphone market slipped to 13.2 per cent in the second quarter, from 16.6 per cent a year ago, while Android's share rose to 79.3 per cent.
Icahn has been embroiled in a battle over Dell, seeking to block a private equity buyout led by founder Michael Dell, which Icahn says undervalues the company.
The 77-year-old Icahn has fought some of the roughest proxy battles in modern corporate history, ranging from the airline TWA to RJR Nabisco and Blockbuster Video. He also headed a shareholder revolt at Yahoo after the Internet giant rejected a takeover from Microsoft.
Forbes magazine estimates Icahn's net worth at USD 20 billion, earning him 26th place in the 2013 list of the world's wealthiest individuals.
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