The local unit opened marginally lower at 73.19 per dollar against previous close of 73.15. The Indian currency traded a high of 72.93 during intraday trade on Thursday.
On Wednesday, Rupee had finished 10 paise higher.
Oil benchmark Brent Crude was trading 0.18% lower at USD 55.96 as mounting coronavirus cases globally raised demand concerns, although a drawdown in U.S. crude stocks for a fifth straight week capped losses.
The dollar extended its rebound from near three-year lows versus major peers on Thursday, supported by higher U.S. yields, as US President-elect Joe Biden prepared to outline his plans for massive fiscal stimulus.