The BSE Sensex gained 400 points while the rupee rose to a two-week high on Tuesday as receding geopolitical risks from Syria and strong exports in August helped lift the currency.
The rupee was at 64.34/35 to the dollar versus its Friday close of 65.24/25. It rose to 64.30 in session, its highest since Aug. 28.
India's merchandise exports posted double-digit growth in the month of August, while imports were "contained", Trade Secretary S. R. Rao said on Monday, offering some respite for the troubled rupee.
Official data is due later this week.
Bond yields also fell sharply, tracking a drop in crude oil prices.
The 10-year bond yield was down 23 bps at 8.40 %.