The US dollar nursed broad losses early on Tuesday, having come under pressure late in New York as investors bought the euro and drove the Australian dollar to its highest this year.
The partially convertible rupee trading at 60.50/51 per dollar at 0336 GMT, its strongest level since Aug. 12 and higher than its Monday's close of 60.77/78.
Overseas investors bought Indian shares worth 14.65 billion rupees ($240.9 million) and 10.56 billion rupees worth of index futures on Monday, when shares hit a record high.