Fresh dollar sales by exporters amid sustained capital inflows also boosted sentiment, helping the local currency to end two days of losses.
At the interbank foreign exchange market, the rupee opened at 61.54 a dollar from the previous close of 61.83.
It moved in a range of 61.21 to 61.73 before ending at 61.23, a rise of 60 paise or 0.97 per cent. The rupee had gained 73 paise to 61.73 on October 3.
"The rupee was seen trading on a stronger note against the US dollar as last-minute deal in the US helped uplift the sentiments in the global markets," said Abhishek Goenka, CEO of India Forex Advisors. "The dollar was seen weakening...And if it does not show a sustained recovery in the coming few days, then we might see rupee continuing with its gains."
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Goenka also said S&P estimated the US may lose as much as 0.6 per cent of GDP in the fourth quarter due to the standoff. This has led to speculation that the Federal Reserve may maintain its stimulus programme up to even March, he said.
"Dollar came under pressure, along with European shares, as US budget deal gave way to worries over the economic impact of the 16-day government shutdown and prospects of a re-run early next year," said Pramit Brahmbhatt, CEO of Alpari Financial Services India. "Chinese credit agency Dagong downgraded the US sovereign rating...Driving further dollar losses.