The rupee trimmed its initial sharp gains against the American currency but was still up by 2 paise at 63.38 in late morning deals on bouts of dollar selling from exporters.
Earlier, the rupee resumed higher at 63.30 per dollar as against the last closing level of 63.40 at the Interbank Foreign Exchange (Forex) market.
The local currency moved in a range of 63.30 and 63.38 per dollar.
The US dollar index was up by 0.18 per cent at 96.42.
Oils rebounded in Asia early today on bargain-hunting after prices plunged a day yesterday as Greek defiance against austerity measures imposed by its creditors sparked turbulence in global markets.
In the New York market, the euro fell against its main rivals yesterday, but trimmed initial losses scored after Greek voters rejected conditions for a new bailout.
Meanwhile, the benchmark BSE Sensex was trading up by 54 points or 0.19 per cent to 8,262.62 at 1045 hrs.
