The central bank is also stepping-in to buy dollars when the rupee strengthens, further capping gains. Data late on Friday showed India's foreign exchange reserves rose to $317.85 billion as of July 18, the highest since October 2011.
Traders expect the rupee to remain in a narrow range, unless global events flare up. This week analysts will look for U.S.-focused action, including the two-day Federal Reserve meeting ending on Wednesday and non-farm payrolls figures on Friday.
"We expect the pair to remain in a very narrow range for the near term as all the fund flows are getting absorbed easily in the market," said Unnati Parekh, head of currency derivatives at KanjiForex, a forex brokerage in Mumbai.
She predicted a range of 60.05 to 60.35 for the week, barring major international shocks.
The partially convertible rupee closed at 60.1250/1350 per dollar, compared with 60.1025/1125 on Friday.
The local currency market will remain closed on Tuesday on account of a national holiday.
The rupee has remained supported as foreign portfolio investors have invested $5.18 billion in local shares and debt so far in July.
* Rupee ends at 60.1250/1350 per dlr vs 60.1025/1125
* Dlr selling by custodian banks offsets import demand
* INR seen in 60.05 to 60.35 range this week - traders