Foreign banks also sold dollars on behalf of exporters, which aided the rupee's gains, traders said.
Earlier in the day, Reserve Bank of India 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.
"We have sufficient reserves, the current account deficit is low. So I think one shouldn't worry too much about the external side at this point," Rajan said on the sidelines of an industry event.
The rupee fell as low as 60.55, a level last seen on April 29, prompting the central bank to sell dollars through state-owned banks around 60.49 rupee levels, traders said.
"Nationalised (state-run) banks sold dollars at higher levels, may be to check sharp depreciation. The rupee can trade higher towards 59.50/80 levels as exporters are likely to sell dollar above 60 levels," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
The partially convertible rupee ended at 60.03/04 per dollar versus its previous close of 60.1550/1650 on Monday.
Earlier in the day, the local currency traded marginally stronger in the spot offshore NDF market, prompting traders to sell dollars in the domestic spot market to narrow the differential. The spot NDF in Singapore were at 60.07/10 at the time of rupee's close.
Oil futures fell towards $112 per barrel, pressured by signs of a thaw in relations between Iran and the West although market players saw scope for gains if violence in Iraq threatened production from OPEC's second-biggest producer.
India imports nearly two-thirds of its oil needs, leaving its currency especially vulnerable to price swings.
For the near-term, traders expect the rupee to trade in a 59.90-60.30 range. Traders will await the outcome of the U.S. Federal Reserve's two-day meeting on Wednesday to get cues on the timing of interest rate hikes.
In the offshore non-deliverable forwards, the one-month contract was at 60.41, while the three-month was at 60.98.