Billionaire investor Carl Icahn says he has built up a "large" stake in Apple.
Mr Icahn says Apple shares are "extremely undervalued" and wants Apple to carry out a bigger share buyback.
In April, Apple said it would return $100bn (£65bn) to shareholders by the end of 2015, by raising its dividend and buying back shares.
Mr Icahn said he had a "nice" conversation with Apple's chief executive Tim Cook and plans to speak to him again shortly.
A US media report said that Mr Icahn's stake is worth well over $1bn, making it one of his biggest shareholdings.
Since hitting a record high in September 2012, Apple shares have fallen 30%.
The announcement helped to boost those shares, which were up more than 5%.
Mr Icahn is known for his aggressive investment style, which involves taking large stakes in firms and pushing managers to change direction.
He is currently involved in a high profile battle to prevent Michael Dell buying back the company he founded.
Mr Icahn claims his plan offers better value for Dell shareholders.
Source: BBC News - Business http://www.bbc.co.uk/news/business-23690125#sa-ns_mchannel=rss&ns_source=PublicRSS20-sa
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