SAN FRANCISCO — Activist investor Carl Icahn says 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 in two messages posted Tuesday on his Twitter account. Until now, he had been deploying Twitter as a weapon in his attack on 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.

Icahn, 77, probably has won some fans among Apple shareholders. After he tweeted, Apple’s market value rose by about $13 billion.

In April, Apple pledged to spend $60 billion buying back its stock through the end of 2015.

Apple also plans to dole out more than $10 billion in shareholder dividends each year.

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.