The rupee appreciated 19 paise to 75.84 per dollar on Tuesday opening bell, tracking gains in Asian currencies amid positive opening in the domestic equity market.
Forex traders said where weak US currency supported the rupee, rising coronavirus cases worldwide and in domestic grounds weighed on the domestic unit.
The rupee opened strong at 75.89 per US dollar, then further gained up 19 paise to 75.84 over its previous close of 76.03 against the greenback on Monday.
"Recovery in the equity markets could spill over to the currencies. Most Asian equity markets are trading with gains this Tuesday morning along with firm US equity futures," Reliance Securities said in a research note.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.17 per cent to 96.54.
"US dollar was flat to lower this morning in Asian trade, after the US Fed announcement on bond purchases," the note added.
The Fed launched its Main Street Lending Program and an emergency lifeline under which it will buy up to USD 750 billion in corporate bonds.
The 30-share BSE benchmark Sensex was trading 605.32 points higher at 33,834.12 and broader NSE Nifty rose 216.55 points to 10,030.25.
Foreign institutional investors were net sellers in the capital market as they sold shares worth Rs 2,960.33 crore on Monday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.45 per cent to USD 39.54 per barrel.
Meanwhile, investor sentiment remained fragile amid rising coronavirus cases across the world.
The number of cases around the world linked to the disease has crossed 80.18 lakh and the death toll has topped 4.36 lakh.
In India, the death toll due to COVID-19 rose to 9,900 and the number of infections rose to 3,43,091.