The shareholders have asked for commitments from the group’s boards that they use their strong balance sheets to return cash to investors.
The investors are said to have moved to pre-empt another spate of deals in the mining sector that analysts and investment bankers have predicted.
Some shareholders have told the companies they were prepared to vote down the re-election of key board members if they did not agree to the commitments.
BHP, the world’s largest miner, scrapped a hostile offer for Canadian fertiliser maker Potash in November and revived a $4.2bn (£2.6bn) share buyback.
Over the last five years the company has returned $25.7bn to shareholders in dividends and buybacks.
Rio is in talks with Africa-focused coal miner Riversdale over an agreed $3.9bn bid.
BHP and Rio both declined to comment.