Mr Icahn also warned that private investors were at risk from the "ridiculously high" junk bond market, likening the situation to the housing bubble in 2008. He is the latest high-profile investor to warn about junk bonds on the programme after DoubleLine founder Jeffrey Gundlach said last month they were brewing a financial crisis.
Mr Icahn's initial stake was valued at about $1 billion in August 2013 but he added to that by early 2014, taking his stake to $3 billion. In February he said he owned about 53 million shares, the value of which had by then climbed to $6.5 billion.
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Apple's stock rose 3 per cent on Friday to close at $128.95, near its all-time intraday high of $134.54, despite falling back earlier in the week after Monday's earnings.
Even at these levels, Mr Icahn said that its share price was "absurd". He has previously suggested that the group's valuation could increase to $1tn. He plans to publish an "in-depth report" on Apple in the coming weeks, he said on Twitter last week, suggesting the company was still "misunderstood" by Wall Street.
But Mr Icahn said he still wants Apple to buy back more of its own stock. "I'd always like to see bigger buybacks," he said.
Mr Icahn also used the television show to reiterate his backing of chief executive Tim Cook's leadership of Apple after it reported record iPhone sales and profits for its quarter ended March, thanks largely to growth in China.
When Mr Icahn first took a position in Apple, "there were guys calling me and saying, 'We've got to get rid of this Tim Cook'," Mr Icahn said. "I met him and he's great . . . guy lives this, he breathes it, he's obsessed with it."
He admitted his bet on Apple was not without risk. "Could something happen? Yeah — this isn't a game that can't lose," he said, noting that Apple's stock price had fluctuated dramatically in the past few years.
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Mr Icahn also said he is "very concerned" about the wider stock market rising too high. "You have a situation where this market keeps going up and up with zero interest rates, and that's what's really pushing it," he said. "Yet a lot of the economic news is not really good and also, perhaps more importantly, earnings are not really good."
He added that he was more worried about the bond market, where private investors are buying in growing numbers in the hope of higher yields.
"What is even more dangerous than the stock market is the high-yield market, the junk bonds market. It's ridiculously high," he said, predicting that default rates would soon rise.
With the US Federal Reserve preparing to raise interest rates, companies with high debt loads may begin to struggle to refinance their liabilities, at a time when many in the US are already being hit by the dollar's strength.
"I'm not going to tell you it's going to be '08, I can't predict year to year," Mr Icahn said. "But you worry about the system and what's going on."