But not every Apple shareholder agrees with that strategy, and at least one big one doesn't appreciate Icahn's activism.
"It's the tail wagging the dog. [Icahn's] recent letter was rambling and contradictory," says Anne Simpson, senior portfolio manager of investments and director of corporate governance for the California Public Employees' Retirement System.
CalPERS is the largest pension fund in the United States with more than $285 billion in assets under management, and it owns close to $1.6 billion in Apple shares.
"There are owners, raiders and traders. We're an owner and have been of Apple for a very long time. Mr. Icahn is a raider and he's an echo chamber who engages in megaphone diplomacy," Simpson added.
Simpson's comments come as Carl Icahn tweeted Tuesday that he "just bought $500 mln more $AAPL shares. My buying seems to be going neck-and-neck with Apple's buyback program, but hope they win that race." With his most recent purchase, Icahn's Apple holdings are roughly worth $4.1 billion.
CalPERS is not the only Apple shareholder who's doesn't think Ichan's call for a buyback is good for the company, or its stock.
"It's not always in the shareholders best interest for the cash hoard to be returned to shareholders," said Matt Patsky, CEO of Trillium Asset Management, which owns 44,000 Apple shares worth more than $20 million.
"Apple is resistant to depleting its cash reserve and they have that right," he said.
Several calls to Icahn were not returned.
Icahn has repeatedly urged the company to put its cash hoard of $158 billion to use by buying back an additional $150 billion of its own stock. Apple in May say it would return $100 billion to shareholders over three years, through a combination of stock buybacks and a quarterly dividend of $3.05 per share.
Apple CEO Tim Cook rejected Icahn's proposition during a dinner last September,which the activist investor called "testy."
(Read more: Apple drops 5% on weak iPhone sales, revenue outlook)
Simpson called Icahn's ideas about Apple's future product strategy as "not clear." She said CalPERS isn't counting on Icahn to provide a vision of what Apple needs to do with future products like Apple TV and the potential iWatch.
"It's troubling for Silicon Valley, if short-term activists interfere with the long-term strategy of some of America's most innovative companies," Simpson said.
—By CNBC's Mark Berniker. Follow him on Twitter @markberniker.