The domestic unit resumed lower at 62.84 per dollar as against the last weekend's level of 62.66 at the Interbank Foreign Exchange market on initial strong buying.
However, it trimmed its losses and was quoted at 62.77 per dollar at 1045 hours as Economic Affairs Secretary Arvind Mayaram said that there is no need to worry about rupee's decline as "economic fundamentals are very strong".
It hovered in a range of 62.73 and 62.85 per dollar during the morning trade.
In New York, the dollar was strong against emerging market currencies such as the Turkish lira and South African rand on last Friday as worries about a Chinese slowdown and prospects of rising US rates triggered a broad flight out of emerging-markets assets.
The Chinese manufacturing sector showed an unexpected contraction in January, heightening fears about the future of emerging-market economies that depend on China for trade or its demand for commodities.
Meanwhile, the benchmark Sensex dropped 324.34 points or 1.53 per cent to 20,809.22 at 1045hrs due to fall in the global market.