Activist investor Carl Icahn meant to encourage Apple to boost its share repurchase program by writing an open letter to the tech giant's CEO Tim Cook, Icahn told CNBC on Tuesday.
"The one thing I disagree with the company on is not buying a great deal more stock here," Icahn said in an interview on CNBC's "Fast Money: Halftime Report."
In the Monday letter, Icahn—who owns more than 52 million Apple shares—valued the company at $240 per share, nearly double its current price. Icahn's suggested value would make Apple worth nearly $1.5 trillion.
Read MoreIcahn: Apple remains undervalued, worth almost double current price
He called for accelerated stock buybacks, and reiterated Tuesday that he did not intend to recommend Apple to investors. The tech giant last month said it would increase its share repurchase authorization to $140 billion from $90 billion announced last year.
With its cash horde—about $194 billion as of last month—Apple has much more leverage to repurchase stock, Icahn contended.
His valuation of the company partly rests on a fiscal 2016 forecast for earnings per share of $12 (excluding net interest income). Icahn added in the letter that he believes Apple will enter and "dominate" new product categories including television and automobiles.
Icahn said Tuesday he still believes Apple will go into the high-definition television market despite a Wall Street Journal report saying the company has shelved its plans for the product.
Regardless of Apple's television plans, it remains "very hard to compete with" because of its ecosystem of products, Icahn contended.
Icahn has made about $3.4 billion on Apple since August 2013, according to a CNBC analysis of public filings.
Read MoreIcahn nets $3.4 billion on Apple
He also touched on his $100 million investment in ride-hailing company Lyft. Icahn said he believes the start-up's driver and trip growth justify more investment and a higher valuation, especially as rival Uber accumulates huge funding.
Uber is reportedly valued at about $50 billion, while Lyft's valuation sits at roughly $2.5 billion.
—CNBC's Lawrence Delevingne contributed to this report.