Indian rupee opened 14 paise lower at 73.16 per dollar on Tuesday versus previous close of 73.02.
On January 4, rupee ended 10 paise higher at 73.02 per dollar against Friday's close of 73.12 per dollar.
At 10:05 IST, the Sensex was down 163.07 points or 0.34% at 48013.73, and the Nifty was down 56.10 points or 0.40% at 14076.80.
"The Indian Rupee closed higher against the US Dollar, due to broad decline in the dollar index. The minutes of the December Fed meeting due this week could reinforce that dovish stance which could continue to weigh on the greenback. FPI bought USD 168 million in local equity to help domestic pair to be on the higher side. However, rising Covid-19 cases push investors towards safe haven," Kshitij Purohit, Lead Currency & Commodities at CapitalVia Global Research.
"Technically USDINR Spot took the support of 72.80 and is facing the resistance of 73.20 levels. Closing above 73.20 will indicate that bullish trade will continue towards 73.50-73.60 level. Support for the pair is 72.80 levels below it can go 72.50 levels," he added.
The dollar found support as concerns about surging COVID-19 cases and uncertainty about U.S. runoff elections in Georgia fueled demand for safer assets.
Oil prices were little changed on Tuesday after OPEC and allied producers, including Russia, continued deadlocked talks on February output while fuel demand concerns lingered on amid new COVID-19 lockdowns.
"USDINR was well bid yesterday at 72.90 by RBI while all others were sellers. We have two events today in the US the effect of which could be seen in coming days. One is the Senate run off and second is the Congress Confirmation of President Biden. Trump may actually disrupt the second event and could result in some risk aversion. For the day USDINR should be sold above 73.20 as stock markets have not fallen much. Importers may cover near 73.00 level," said Anil Kumar Bhansali, Head - Treasury, Finrex Treasury Advisors.