Concerns that foreign investors will exit from developing economies as the Fed scales back bond purchases, along with fears of a slower Chinese economy, have roiled markets from Turkey to South Africa and Brazil since last week.
Turkey and South Africa responded by raising interest rates this week to help support their currencies. The Reserve Bank of India also tightened monetary policy, although that action was aimed at pushing down high consumer inflation.
"International monetary cooperation has broken down," Rajan, told Bloomberg TV India in an interview broadcast late on Thursday.
"Industrial countries have to play a part in restoring that, and they cannot at this point wash their hands off and say we will do what we need to, and you do the adjustment you need to."
Rajan, a high-profile former chief economist at the International Monetary Fund, took charge at the Indian central bank on September 4 amid the country's worst financial crisis since 1991.
The Fed on Wednesday trimmed its monthly bond purchases by another $10 billion, despite the turmoil in emerging markets. The action was widely expected, although some investors had speculated that the U.S. central bank might put its plans on hold given the jitters overseas.
The so-called tapering marks the wind down of a period of easy money first ushered by the Fed in response to the 2008 global financial crisis.
Emerging market policy makers have long complained that the Fed's massive money printing had triggered a wave of funds into their countries, inflating risk assets and raising the threat of destabilising flows once the Fed started to withdraw that stimulus.