Besides, robust US dollar against its key rivals also had an impact on the domestic unit.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.42 per cent to 97.02.
The rupee opened at 75.53 against the US dollar, but pared the gains to settle at 75.61 against the US dollar, down 6 paise over its previous close.
During the four-hour trading session, the domestic unit saw an intra-day high of 75.43 and a low of 75.61.
On the equity front, the benchmark Sensex closed 413.89 points or 1.20 per cent lower at 33,956.69.
Likewise, the NSE Nifty ended 120.80 points or 1.19 per cent down at 10,046.65 as an uncertainty about economic revival amid mounting COVID cases in the country hung heavy on investor minds.
Foreign institutional investors were net buyers in the capital market as they bought shares worth Rs 490.81 crore on Tuesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 1.27 per cent to USD 40.28 per barrel.
Forex traders said rupee surrendered its intra-day gains due to dollar buying by banks and oil importers.
"Traders refrained from placing aggressive bets in favour of the rupee due to concern over India's macroeconomic fundamentals and caution continue after the Reserve Bank of India's dollar-buying interventions in the spot market around 75.40 per dollar of late," said
Jateen Trivedi, Senior Research Analyst (Commodity & Currency) at LKP Securities.
According to Devarsh Vakil, Deputy Head of Retail Research, HDFC Securities, traders are weighing the global stock rally amid still challenging economic conditions.
"The strong dollar inflows supporting rupee while rise in COVID-19 cases after Unlock-1 and weaker economic data weighed down on rupee," Vakil said.
The number of cases around the world linked to the disease has crossed 71.38 lakh and the death toll has topped 4.06 lakh.
In India, the death toll due to COVID-19 rose to 7,466 and the number of infections rose to 2,66,598, according to the health ministry.
"On overseas front, the re-escalation of tensions in the Korean peninsula and US Federal Open Market Committee (FOMC) meeting will be in focus for near term trend in dollar index," Vakil said.
Meanwhile, the Financial Benchmark India Private Ltd (FBIL) set the reference rate for the rupee/dollar at 75.6307 and for rupee/euro at 85.3523. The reference rate for rupee/British pound was fixed at 96.0258 and for rupee/100 Japanese yen at 69.05. DRR MKJ MKJ