The rupee appreciated by 3 paise to close at 83.33 (provisional) against the US dollar on Tuesday on positive domestic markets and a soft American currency.
At the interbank foreign exchange market, the local unit opened at 83.37 against the greenback. The unit hit an intra-day high of 83.28 and a low of 83.39 against the greenback.
The domestic unit finally settled at 83.33 (provisional) against the dollar, 3 paise higher from its previous close.
On Monday, the rupee appreciated by 8 paise to close at 83.36 against the US dollar.
"Indian rupee appreciated on Tuesday on weak US dollar and positive domestic markets. However, a recovery in crude oil prices and FII outflows capped sharp gains," said Anuj Choudhary, Research Analyst, Sharekhan by BNP Paribas.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.01 per cent lower at 106.06, on easing tensions between Israel and Iran.
Brent crude futures, the global oil benchmark, advanced 0.29 per cent to USD 87.25 per barrel.
"We expect the rupee to trade with a slight positive bias on improved global risk sentiments and easing of geopolitical tensions in the Middle East," Choudhary said.
Easing dollar on strong euro and pound amid mixed to positive PMI data from Europe also supported the rupee.
"However, any fresh aggressions in the Middle East may cap sharp upside. Traders may take cues from PMI data from US. Investors may remain cautious ahead of inflation data from US later this week. USD-INR spot price is expected to trade in a range of Rs 83.10 to Rs 83.50," Choudhary added.
On the domestic equity market front, Sensex advanced 89.83 points, or 0.12 per cent, to settle at 73,738.45 points. The Nifty rose 31.60 points, or 0.14 per cent, to close at 22,368.00 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday, as they offloaded shares worth Rs 2,915.23 crore, according to exchange data.
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