NEW YORK (Reuters) - Activist billionaire investor Carl Icahn said Tuesday on CNBC that his firm has $2 billion invested in shares of technology giant Apple Inc.. Shares of Apple rose over 2 percent on Tuesday on news that 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. Icahn said on CNBC that Apple's chief financial officer was also in attendance at the dinner with Cook on Monday. (Reporting by Sam Forgione; Editing by Chizu Nomiyama)