Rupee in Tuesday's trade opened tad higher at 71.37 versus previous close of 71.44.
Oil again has headed lower for the sixth consecutive day as the spread of a new virus raised concerns of yet again slowing economy and weak demand for the commodity. Brent crude was down 15 cents, or 0.3%, to $59.17 at around 0114 GMT.
On Monday, the rupee ended lower as risk appetite ebbed in view of the widening spread of coronavirus as well as fatalities on account of it.
In the pre-opening trade after a significant fall on Monday, markets are trading with a positive bias.