The rupee continued to decline against the dollar in late morning trade and was quoted lower by 13 paise at 63.65 on sustained demand of the American currency from banks and importers due to its rising strength in the overseas market.
The rupee resumed lower at 63.62 as against the last weekend's level of 63.52 at the Interbank Foreign Exchange (forex) market and dropped further to 63.67 before quoting at 63.65 at 1045 hours.
It moved in a range of 63.67 and 63.59 during the day.
In the New York market, the dollar recorded its first weekly gain against the euro in five weeks last Friday, wrapping up the week up 3.4%.
Meanwhile, the benchmark BSE Sensex dropped 113.57 points, or 0.41 per cent, to 27,843.93 at 1045 hours.
Crude prices rose on bargain-hunting in Asia today after sliding last week, but a supply glut and a resurgent dollar are likely to cap gains, analysts said.
US benchmark West Texas Intermediate for July delivery climbed 14 cents to $59.86 a barrel and Brent crude for July added eight cents to USD 65.45 in late-morning trade.