Shares of Apple Inc. rose about 2 percent on Tuesday on news that billionaire activist-investor Carl Icahn had dinner with Apple chief executive Tim Cook on Monday and "pushed hard" for a buyback.

"Had a cordial dinner with Tim last night. We pushed hard for a 150 billion buyback. We decided to continue dialogue in about three weeks," Icahn tweeted on Tuesday.

In August, Icahn told Reuters that "Apple has the ability to do a $150 billion buyback now by borrowing funds at 3 percent.

He also said at the time, "If Apple does this now and earnings increase at only 10 percent, the stock - even keeping the same multiple currently - should trade at $700 a share."

Tuesday, shares of Apple rose 1.85 percent to trade over $485 a share.

A source familiar with the matter, who declined to be named because Icahn hasn't disclosed his holdings in Apple, said the investor's stake was worth around $1 billion, a fraction of the company's market value of more than $400 billion.

Cook did not mention the dinner in any tweets on Tuesday. (Reuters)