However, strong recovery in the equity market restricted the rupee's fall, forex dealers said.
The rupee resumed at yesterday's closing level of 63.60 at the Interbank Foreign Exchange (Forex) and hovered in a restricted range of 63.55 and 63.63 before finishing at 63.62, showing a loss of just two paise, or 0.03 per cent, from its last close.
The dollar index was trading lower by 0.01 per cent against its major global rivals today.
In New York market, the euro strengthened yesterday despite reports that Greece's creditors had rejected negotiators' latest reform proposal, sparking a sell-off in Greek bonds and European equities.
Meanwhile, the benchmark BSE Sensex recovered by 166.30 points, or 0.60 per cent, to close at 27,895.97.