The dollar's weakness against other currencies overseas also supported the rupee sentiment, a currency dealer said.
The moved between 63.98 per dollar and 63.93 per dollar at the interbank forex market in early trade.
The dollar fell further against the yen to hit a 15-month low in Asian trade while the euro gained after a firm German growth.
Yesterday, the rupee had gained 23 paise to close at 64.09 a dollar on sustained selling of the American currency by exporters and banks.