The domestic unit hovered in a range of 61.33 and 61.58 per dollar during the morning deals.
The BSE benchmark Sensex resumed higher at 20,915.76 and firmed up further to 20,970.92, but declined immediately to 20,831.17 before quoting at 20,861.65 (1045hrs), showing a loss of 21.24 points, or 0.14%, over the weekend level.
Oil prices edged higher by 10 cents to USD 100.91 a barrel in Asian trade today as dealers await long-delayed US economic data for clues about the health of the world's largest crude consumer, analysts said.
The US stimulus programme has been credited with fuelling a global equities rally for most of the year.
The US Central bank said in September that it would not wind down the programme if there was no broad improvement in the world's largest economy.