The pair had closed at 60.1550/1650 per dollar on Monday.
RBI Governor Raghuram Rajan said the country is watching the Iraq situation, but despite the uncertainty the domestic economy is better prepared to deal with any shocks on the external front.
The pair had earlier risen to 60.55, a level last seen on April 29, but came off after the RBI was spotted selling dollars through state-owned banks around 60.49 rupee levels, traders said.
Brent crude futures held near $113 per barrel as concerns over oil supply persisted, with the United States considering air strikes in Iraq amid a worsening security situation in the key oil producing country.
The partially convertible currency is seen trading in a range of 60.00 to 60.55 during the session.