Hardening further for the third straight day, the rupee advanced another 18 paise to 68.24 against the dollar in early trade on Tuesday on sustained selling of the US currency by banks and exporters.
Besides, the dollar's weakness against some currencies overseas supported the rupee.
Forex dealers said rebound in domestic stock markets also helped the domestic unit.
On Monday, the rupee had gained 20 paise to close at 68.42 against the dollar, enthused by budgetary proposals to boost exports.