Forex traders said the government's decision to open COVID vaccination to all above 18 years from May 1 lifted investor sentiment.
At the interbank forex market, the local unit opened at 74.65 against the US dollar, then gained some strength to quote at 74.64, a rise of 23 paise over its last close.
In the previous session, the rupee had settled at 74.87 against the American currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.14 per cent to 90.94.
The Indian rupee started this Tuesday on a stronger note against the US dollar, tracking the overall weakness of the dollar, Reliance Securities said in a research note.
"Gains could be capped by the surge in coronavirus infections leading to stricter lockdowns and in turn hampering the recovery of the economy," the note said.
However, hopes for COVID-19 vaccination from May to all above 18 years could stem the rise of infections and limit the damage caused to the economy and cap weakness of the currency, it added.
Meanwhile, global oil benchmark, Brent crude futures, rose 0.95 per cent to USD 67.69 per barrel.
On the domestic equity market front, the BSE Sensex was trading 278.33 points or 0.58 per cent higher at 48,227.75 in early deals, while the broader NSE Nifty rose 87.40 points or 0.61 per cent 14,446.85.
Foreign institutional investors were net sellers in the capital market on Monday as they sold shares worth Rs 1,633.70 crore, as per exchange data.