In active trade at the Interbank Foreign Exchange (forex) market, the local currency resumed higher at 39.36/38 a dollar from Friday's close of 39.440/4550 a dollar but later eased marginally to 39.38/39 a dollar in late morning deals.
Rupee sentiment was also aided by dollar weakness overseas and a likely rate cut by the US Federal Reserve in its meeting on October 31.
There was fairly good month-end dollar demand from oil refineries in early trade in the light of spiraling crude oil prices, which touched a new record of USD 93 a barrel in New York, forex dealers said.
It was quoted at about USD 92.69 a barrel in Asian trade on Monday morning.
The benchmark Sensex flared up by 616 points to touch an all-time high of 19,859.47. Asian indices were also up in the range of 0.75 per cent and 3.5 per cent in early trade.