The rupee on Friday strengthened further by 20 paise to 65.81 against the dollar in early trade, largely supported by recent RBI measures.
Meanwhile, the BSE benchmark index Sensex rose by 126.10 points, or 0.66 per cent, to 19,105.86 in opening trade.
The domestic currency had gained 106 paise to close at 66.01 yesterday against the dollar after steps taken by new RBI Governor Raghnuram Rajan to attract US currency inflows.
To support the rupee, RBI announced steps such as enhanced limits for exporters to re-book cancelled forward exchange contracts and a special concessional window to swap foreign currency non-resident (FCNR) deposits.
Dealers said besides increased dollar selling by exporters, a higher opening in domestic equity market and dollar's weakening against some currencies overseas helped the rupee rise.