The rupee edged up 3 paise to 64.02 against the dollar on Tuesday as the US currency lost some muscle overseas.
Exporters and banks stayed away from the American currency as capital inflows jumped.
The dollar’s lustre dimmed against other currencies globally, which supported the local unit.
In the opening session, the domestic unit was up by 3 paise at 64.02. On Friday, it had ended flat at 64.05.
Stock benchmark Sensex rose 65.07 points, or 0.19 per cent, to a record high at 34,005.37 and the Nifty went up 22.10 points, or 0.21 per cent, to a new peak of 10,515.10 in early session on Tuesday.