The rupee opened weak at 64.21 a dollar and touched a low of 64.24 a dollar in early session amid falls in stock markets. It moved in a range of 64.18 a dollar to 64.24 a dollar in morning trade.
The rupee had lost 7 paise to settle at 64.12 a dollar yesterday, marking it third straight day of fall against the dollar.
Dealers said increased demand for the American currency from importers and banks and losses in domestic equity markets weighed on the rupee.
Worries about North Korea weighed on global stocks and the dollar which fell against the Japanese yen.
The benchmark BSE Sensex fell 223.02 points, or 0.70 per cent, to 31,586.53 in early trade today.