MOSCOW (Reuters) - Prime Minister Dmitry Medvedev offered rare criticism of President Vladimir Putin's methods of dealing with business leaders on Friday, heightening speculation of a growing rift between Russia's top two rulers.

Medvedev spoke a few days after Putin issued a stinging rebuke of his former protege's government by accusing cabinet ministers of failing to act on his orders and criticizing its fiscal plans.

In a speech at a showcase business forum in the Black Sea city of Sochi, Medvedev referred to an incident in 2008 when Putin, then serving as prime minister, promised to "send a doctor and a prosecutor" to the billionaire owner of steel and coal producer Mechel who had been unable to attend an industry meeting because of illness.

The comments directed toward Igor Zyuzin came to be known as one of Putin's harshest attacks ever on a powerful business figure and caused the company's stock to plummet.

"I think that in modern Russia, if we talk about business, unequivocal orders are being made in different ways, let's say, in proposals to send a doctor in for a cure," Medvedev said on Friday. "Russian business knows what I mean ... I wish we (would) start learning to live in a different way."

In 2010 Putin said he regretted the comments.

In early 2011, when he was still president, Medvedev appeared to publicly rebuke Putin for comparing Western calls for action on Libya with the medieval Crusades.

While cautious, Medvedev's words on Friday seemed to be one of his first public barbs at Putin since the two swapped jobs in May and could signal more serious disagreements over policy in the early part of Putin's third term as president.

Faced with constitutional limitations on serving a third straight term as president, Putin steered Medvedev, a lawyer, into the Kremlin in 2008, while Putin himself served four years as prime minister.

At the time, the two said they ruled in "tandem", a reference to Putin's powerful presence in state decision making.

After Putin's criticism of cabinet activity this week, Medvedev coolly listened the following day to ministers propose dipping into dividends paid by state energy firms and reducing the size of the oil revenue fund.

But a host of new laws engineered by Putin has given rise to suspicions that the president is trying to undermine Medvedev's legacy and may soon rid himself of the man once widely seen to be his protege.

New legislature is set to tighten the Kremlin's controls on the Internet and another will force foreign funded non-governmental organizations to register themselves as "foreign agents", measures that critics say are clamping down on dissent.

Some analysts believe that while disagreement between Putin and Medvedev may exist, there is no real rupture in their relationship and their occasional political back and forth is meant to give the appearance of plurality under Putin, who is known for his top-down approach to decision-making.

While the public disagreements have increased speculation that Putin is planning on firing Medvedev to assemble a stronger government, Putin has shown himself in the past to reward loyalty, one of Medvedev's strongest traits.

(Editing by Mark Heinrich)