Dollar sales by exporters amid positive local stocks also supported the rupee, which is up 107 paise, or 1.71 per cent, this past week.
At the interbank foreign exchange market, the rupee resumed lower at 61.85 and dropped to a low of 61.95 on initial hesitancy in local equities.
It bounced back to a high of 61.25 before closing at 61.44, a gain of 29 paise or 0.47 per cent. It was the highest close for the rupee since reaching 61.43 on August 14.
The US government shutdown entered its fourth day today as efforts to break the political standoff between Republicans and Democrats over the budget failed to make any headway.
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Foreign investors may pull out from emerging markets, including India, if the Fed eases its monthly USD 85 billion bond-buying programme as the US economy revives.
The 30-share S&P BSE Sensex closed up 13.88 points after a choppy session as talks on the US budget and debt limit continued without any indication of a resolution. Foreign institutional investors bought a net USD 188.26 million of shares yesterday, as per Sebi data.