Domestic traders were also enthused after Finance Minister Nirmala Sitharaman hinted at more stimulus measures.
Forex traders said rupee was trading in a narrow range as market participants remained cautious ahead of the Brexit summit.
Amid sustained foreign fund inflows, easing global crude prices also helped buying sentiment, traders said.
Foreign fund inflows also supported the local currency, a forex trader said.
The broader NSE Nifty rose 35.70 points, or 0.31 per cent, to settle at 11,464.
Silver also jumped by Rs 489 to Rs 46,809 per kilogram here from its previous close of Rs 46,320 per kilogram.
US West Texas Intermediate (WTI) crude CLc1 had gained 16 cents or 0.3 per cent to USD 52.97 a barrel.
At the interbank foreign exchange, the rupee opened at 71.60 then fell to 71.71 against the US dollar.
The 30-share index was trading 158.41 points, or 0.41 per cent, higher at 38,664.50.
After soaring 421 points during the day, the 30-share Sensex ended 291.62 points, or 0.76 per cent, higher at 38,506.09.