The benchmark BSE Sensex rallied 178 points, or 0.52%, to trade at an all-time high of 34,331.85 and the NSE Nifty breached the 10,600 for the first time in opening trade Monday.
The rupee strengthened by 11 paise to trade at 63.26 against the US dollar in the opening session on selling of the greenback by exporters and banks amid gains in stocks which scaled record levels.
Currency, dealers said continued foreign fund inflows and weakness in the greenback against other currencies overseas supported the rupee.
Furthermore, a higher opening in the domestic equity market gave the uptrend some momentum, they added.
On Friday, the rupee ended at a 32-month high of 63.37, up 4 paise on steady unwinding of the American currency by exporters.