The local currency resumed higher at 60.10 per dollar as against the last weekend's level of 60.18 at Interbank Foreign Exchange (Forex) market on initial selling of dollars by banks and exporters in view of recovery in the equity market.
However, it failed to maintain initial gains and was quoted at 60.19 per dollar at 1000 hours on some demand for the American currency from banks.
It hovered in a range of 60.05 and 60.21 per dollar during the morning deals.
Crude oil prices edged higher in Asian today on continued violence in Iraq, but gains were capped as the risk premium associated with the crisis in the key crude producer is already factored in, analysts said.
The US benchmark West Texas Intermediate was up 31 cents to USD 107.14.
In New York market, the dollar rebounded on Friday, but posted weekly losses against most major rivals after the Fed signalled this week it was likely to keep interest rates low for a while.
Meanwhile, the benchmark Sensex recovered by 29.93 points, or 0.12 per cent, to 25,135.44 at 1000 hours.