The local unit opened at 73.94 against the greenback and gained further to touch 73.67, registering a rise of 38 paise over its previous close.
On Friday, the rupee has settled 17 paise lower at 74.05 against the US dollar.
Oil prices slipped on Tuesday amid concerns over mounting supply after leading producers delayed talks on 2021 output policy that could extend production cuts as the coronavirus pandemic continues to sap fuel demand, according to the Reuters report.
However, prices recovered in the afternoon and Brent Crude Futures, the global oil becnhmark, was trading marginally higher at 47.98. (3.57 pm).