The rupee weakened by 20 paise to 61.93 against the dollar in early trade today on the Interbank Foreign Exchange market. Dealers said, fresh demand for the US currency from importers put pressure on the rupee, but a higher opening in the domestic equity market and dollar's weakness against other currencies overseas capped the fall. The rupee had appreciated by 73 paise to close at an almost seven-week high of 61.73 against the dollar in the previous session as the US currency weakened globally.