The rupee added another 11 paise to trade at 73.38 against the US dollar in opening session on Tuesday in line with stronger Asian peers and positive domestic equities.
The sustained foreign fund inflows also supported the rupee, traders said.
At the interbank forex market, the domestic unit opened at 73.42 against the US dollar, then inched higher to 73.38 against the greenback, registering a rise of 11 paise over its previous close.
On Monday, the rupee had settled at 73.49 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.24 per cent to 90.11.
"The phase of weak USD, steepening US yield curve, lower US real rates, stronger equities, stronger commodities and stronger EM assets continues," said Abhishek Goenka, Founder and CEO, IFA Global.
Goenka further said that "today is the December exchange traded currency derivatives' expiry. Given the high open interest on account of RBI intervention we could see a lot of selling interest at the RBI fix in OTC."
Meanwhile, Asian currencies are trading stronger against the USD.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 347.51 points higher at 47,701.26, and the broader NSE Nifty advanced 90.20 points to 13,963.40.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 1,588.93 crore on a net basis on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, rose 0.45 per cent to USD 51.09 per barrel.