The rupee/dollar pair was at 54.48/49 versus its previous close of 54.0750/0850.
Local shares are down 0.95 per cent, headed towards their biggest daily percentage fall in two months.
"There was some dollar buying before the daily RBI reference setting," says a dealer.
The euro hit a six-week low against the dollar on Thursday, a day after minutes of the Federal Reserve's last policy meeting showed some policymakers thought the Fed may have to slow or stop buying bonds before seeing a pick-up in employment.
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