The rupee ended at 83.3350 against the U.S. dollar, up 0.2% against its previous close at 83.50.
The currency rose to an intra-day high of 83.3350, its strongest since May 3, and ended up 0.2% on the week.
The RBI likely intervened near 83.50 levels earlier in the session to cap weakness in the rupee but interbank dollar sales picked up after the mid-day fix, which helped the currency gain, traders said. The fix is a daily reference rate for the dollar-rupee pair published by the central bank.
The rupee had largely hovered between 83.45-83.50 during the week amid pressure from equity outflows and dollar demand from local oil companies.
Foreign investors have sold over $3 billion worth of Indian equities in May so far on concerns about the outcome of the country's ongoing elections.
The broad range for the rupee continues to be 83.20-83.60 and it is unlikely to see sharp moves before the June 4 election results, said Abhilash Koikkara, head of foreign exchange and rates at Nuvama Professional Clients Group.
The dollar index rose 0.2% to 104.75, while Asian currencies slipped, with the Korean won down 0.5% and leading losses.
"We still think there is not enough thrust from U.S. data to justify a significantly weaker greenback just yet," ING Bank said in a note. "Expect the dollar index (DXY) to trade in the 104-105 range in the near future."
Investors will also keep an eye on remarks from U.S. Federal Reserve officials later in the day for cues on the future path of policy rates.
Indian markets will remain shut on Monday on account of voting in India's financial capital Mumbai.
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