Rupee opening today: The Indian rupee appreciated by 33 paise to 72.43 against the US dollar in early trade on Tuesday tracking positive opening in domestic equities. At the interbank foreign exchange the rupee opened at 72.50, then gained further ground and touched a high of 72.43 against the US dollar, registering a rise of 33 paise over its previous close.

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The domestic currency, however, could not hold on to the gains and was trading at 72.64 against the American unit at 1002 hrs.

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On Monday, rupee had settled at 72.76 against the greenback.

Meanwhile, investor sentiment remained fragile amid concerns over the impact of coronavirus outbreak after two fresh cases of novel coronavirus were detected in India.

India on Monday reported two new cases of the novel coronavirus, including one from the national capital, the Union Health Ministry said as the government stepped up its efforts to detect and check the infection.

The coronavirus outbreak that started in China's Wuhan city in December has killed over 3,000 people in that country with total confirmed cases crossing 80,000 as it continues to spread to new countries around the world.

Meanwhile, domestic bourses opened on a positive note on Tuesday with benchmark indices Sensex trading 458.88 points higher at 38,602.90 and Nifty up by 158.90 points at 11,291.65.

Foreign institutional investors (FIIs) remained net sellers in the capital market, as they sold equity shares worth Rs 1,354.72 crore on Monday, according to provisional exchange data.

Brent crude futures, the global oil benchmark, rose 2.41 per cent to USD 53.15 per barrel.

Meanwhile, the dollar index, which gauges the greenback's strength against the basket of six currencies was trading 0.13 per cent higher at 97.48.

The 10-year government bond yield was at 6.35 per cent in morning trade.