Domestic shares jumped nearly 1.5 per cent on Monday to an all-time high, surpassing their previous record hit just last week, as lenders including ICICI Bank, extended a recent rally.
Foreign funds have bought shares worth $2.3 billion so far in March, taking total inflows in 2014 to $2.6 billion.
"Custodian banks were offering dollars but good bids came in from state-run banks, pulling the rupee off highs," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
"There is good support for the dollar/rupee at 60.50-60 levels. I expect a range of 60.30 to 61.10 for the pair in the rest of the week."
The partially convertible rupee closed at 60.77/78 per dollar compared with 60.8950/9050 on Friday, marking its strongest close against the dollar since Aug. 1.
The unit rose as high as 60.6450 intra-day, its strongest since March 11.
Traders said gains in other Asian units also underpinned sentiment for the rupee after the yuan rebounded from its 13-month low.
In the offshore non-deliverable forwards, the one-month contract was at 61.13, while the three-month was at 61.81.