Forex traders said market participants remained cautious as currency markets will remain shut for the next couple of sessions.
Forex markets will remain shut on April 1 for the annual closing of banks and on April 2 on account of Ram Navami.
The rupee, which opened on a positive note at 75.52, settled for the day down 1 paise at 75.60 against the American currency.
During the day, the domestic unit touched a high of 75.31 and a low of 75.66.
On Monday, rupee had settled at 75.59 against the US dollar.
The rupee has witnessed a sharp decline of over 9 per cent in fiscal year 2019-20. The local unit has depreciated by 646 paise or 9.34 per cent in FY20. On March 29, 2019, the rupee was quoted at 69.14 to the dollar.
Besides, the domestic unit suffered significant loss in the January-March quarter.
"The rupee marked the biggest quarterly loss amid foreign fund outflows, weaker domestic economic data and Coronavirus outbreak. Foreigners have withdrawn more than USD 14.5 billion this quarter," HDFC Securities Head PCG & Capital Markets Strategy V K Sharma said.
"Going ahead, the trend in Asian currencies and foreign fund flows will decide the action in rupee. Spot USD/INR is having near-term support at 74.70 and resistance at 76.30," Sharma added. DRRMKJ