Forex traders said price action remains subdued as investors are awaiting the Reserve Bank of India''s (RBI) policy decision and the US non-farm payrolls data on Friday for further cues.
At the interbank foreign exchange, the domestic unit opened at 74.36 against the dollar, then inched higher to 74.30, registering a gain of 4 paise over its previous close.
On Monday, the rupee had settled at 74.34 against the US dollar.
"Rising COVID-19 infections in Asian countries could continue to keep appreciation limited," Reliance Securities said in a research note.
Asian currencies have started mixed this Tuesday morning, while crude remains subdued and could cap depreciation bias, the note added.
Meanwhile, the dollar index, which gauges the greenback''s strength against a basket of six currencies, was trading 0.03 per cent down at 92.02.
"USD-INR is being bought by RBI and therefore the stability is seen with a 10-15 paise movement. All other market participants are sellers. Market seems to be keenly awaiting for the MPC meeting starting tomorrow," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.
On the domestic equity market front, BSE Sensex was trading 294.94 points or 0.56 per cent higher at 53,245.57, while the broader NSE Nifty advanced 70.65 points or 0.44 per cent to 15,955.80.
Meanwhile, foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 1,539.88 crore, as per exchange data.
Global oil benchmark Brent crude futures declined 0.04 per cent to USD 72.86 per barrel.