The rupee on Tuesday rose 14 paise to 62.46 against the dollar, supported by better-than-expected current account data and a weakening US currency.
Fresh dollar sales by exporters also helped the rupee.
However, capital outflows capped the gains, a dealer said.
The rupee resumed stable at the previous closing level of 62.60 a dollar and touched a low of 62.61 at the interbank foreign exchange market. It later climbed to a high of 62.17 as local equities recovered and exporters sold dollars.
The rupee pared its mid-session gains on late dollar demand from importers and fell to settle at 62.46, a rise of 14 paise or 0.22%.
Traders said the US government shutdown is seen having a negative impact on economic growth, which may delay the tapering of the Fed's massive bond-purchase programme.
"Yesterday, the current account data was released, which was better than expectations and that helped the rupee to post gains against the US dollar," said Abhishek Goenka, CEO of India Forex Advisors. "It came out at $21 billion against expectations of $23 billion for the April-June quarter. Today, after the news came regarding US government's shutdown, the rupee reacted positively as the US dollar index fell."
The 30-share S&P BSE Sensex firmed up 137.38 points or 0.71%. Foreign institutional investors sold a net $83.55 million of shares yesterday, as per Sebi data.
"Dollar index is losing for the second consecutive day as the US government began a partial shutdown on Tuesday...which helped the rupee to trade strong," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
The dollar index was down 0.21% against key rival currencies after the US government entered a partial shutdown following the failure of lawmakers to break a budget impasse.
Forward dollar premiums fell on fresh receipts by exporters.
The benchmark six-month forward dollar premium payable in March dipped to 268-272 paise from 273-1/2-277-1/2 paise previously and far-forward contracts maturing in September ended lower at 486-491 paise from 493-497 paise.
The RBI fixed the reference rate for the dollar at 62.3555 and for the euro at 84.5365.
The rupee dropped further to 101.37 against the pound from the overnight close of 101.02 and declined to 84.60 per euro from 84.50.
It rebounded against the Japanese yen to 63.92 per 100 yen from 64.12 previously.
The foreign exchange and money markets are closed tomorrow, October 2, on account of Gandhi Jayanti.