SAN FRANCISCO » Activist investor Carl Icahn thinks Apple should be doing more to revive its stock price, and wants to help CEO Tim Cook with the resuscitation.

Icahn, an outspoken billionaire renowned for pouncing on out-of-favor stocks, signaled he has Apple Inc. in his sights. He spoke out on today with a couple of messages posted on a Twitter account that he recently opened to attack Dell Inc.’s proposed sale to a group led by its CEO, Michael Dell.

The Twitter posts announced that Icahn had acquired a large but unspecified stake in Apple and that he had just had a “nice conversation” with Cook about his belief that the maker of the iPhone and iPad should be using even more of its $147 billion in cash to buy back its own stock. Apple spokesman Steve Dowling described Icahn’s discussion with Cook as positive, but declined to elaborate. “We appreciate the interest and investment of all our shareholders,” Dowling said.

In April, Apple pledged to spend $60 billion buying back its stock through the end of 2015 as a way to return some of its cash to shareholders. About $18 billion of that commitment already had been spent through June 29. Apple also plans to dole out more than $10 billion in shareholder dividends each year.

Icahn thinks Apple should be pouring even more money into its stock because he believes the shares are worth more than most investors currently believe, according to his tweet. Despite a recent upturn that has re-established Apple as the world’s most valuable company, its stock remains 30 percent below its peak of $705.07 reached nearly 11 months ago.

As often occurs after Icahn reveals an interest in a company, investors began snapping up Apple’s shares on the hope that the Cupertino, Calif. company might be forced to take steps to appease Icahn or risk the billionaire threatening an attempt to overthrow Apple’s board.

Apple’s stock surged $22.21, or nearly 5 percent, today to finish at $489.87 — its highest closing price in nearly seven months.

Icahn’s tweets gave little inkling about how much input he intends to give Apple. He didn’t immediately respond to an interview request from The Associated Press.

Although he often becomes confrontational with companies that don’t heed his advice, Icahn doesn’t always engage in public hissing matches.

For example, Icahn has been supportive of Netflix Inc. CEO Reed Hastings since he acquired a 10 percent stake in the Internet video service last year. The investment has turned into one of his most successful. The 5.5 million shares that Icahn bought when Netflix was trading near its 52-week low of $53.05 are currently worth about $1.1 billion more than his original investment.

Icahn, 77, has been locked in a bitter battle with Dell as he tries to stop the slumping personal computer maker from selling itself to Michael Dell — a CEO who Icahn thinks should be fired. Using a 9 percent stake in Dell as leverage, Icahn has been leading a stockholder mutiny that resulted in Michael Dell and his main ally, Silver Lake Partners, to raise their initial offer of $24.4 billion, or $13.65 per share, to $24.8 billion, or $13.88 per share, including a special dividend.

Dell hopes to win shareholder approval of the sweetened offer at a Sept. 12 meeting, but Icahn is still fighting in court for the right to hold a separate vote on the same date to replace the company’s board.

Icahn has invested more than $2 billion for a nearly 9 percent stake in Dell. Those holdings are currently worth about $2.15 billion.

Apple’s stock has slumped from its high largely because its growth has slowed while its earnings have been squeezed from tougher competition in the smartphone and tablet computer markets. Although the iPhone and iPad remain popular, Apple has been losing market share as more people buy less expensive devices running on the Android operating system made by Google Inc.

Investors also have been disappointed by Apple’s inability to unveil a breakthrough product since Cook succeeded Steve Jobs as CEO nearly two years ago. Jobs died in October 2011, shortly after anointing Cook as his hand-picked replacement.

Many analysts believe Apple is poised to begin selling a lower-priced version of the iPhone to help boost its sales. The cheaper model could be unveiled next month when Apple is also expected to provide its first peek at the next generation of its top-of-the-line iPhone.