The rupee ended marginally lower by two paise at 63.62 against the US dollar on month-end demand for the American currency from importers.
However, strong recovery in the equity market restricted the rupee's fall, forex dealers said.
The rupee resumed at Wednesday's closing level of 63.60 at the Interbank Foreign Exchange 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 on Thursday.
In New York market, the euro strengthened Wednesday despite reports that Greece's creditors had rejected negotiators' latest reform proposal, sparking a sell-off in Greek bonds and European equities.
Oil prices were little changed in Asian trade on Thursday as an unexpected build in US gasoline inventories offset a higher than forecast draw in US crude inventories, while Brent was supported by buoyant manufacturing figures from Europe.
