The US currency held on to its advantage because of unabated month-end demand from importers and banks amid foreign capital outflows.
The dollar was firm against a few global currencies, but the strength in domestic equities came as a buffer for the rupee losses, analysts said.
In the opening session, the domestic unit fell 10 paise at 64.18. Yesterday, it had ended lower by 3 paise at 64.08 in a quiet trade.
The benchmark BSE Sensex went up 76.71 points, or 0.22 per cent, to scale yet another new peak of 34,087.32 in early session today.