Recovery in equity market also boosted rupee value against dollar, a forex dealer said.
Rupee resumed lower at Rs 66.30 against last Thursday's closing of Rs 66.26 at the Interbank Foreign Exchange (Forex) market and dropped to 66.3775 on initial dollar demand from banks and importers.
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It has gained by 50 paise or 0.75% in six trading days.
It hovered in a range of 66.3775 and 66.10 during the day.
The dollar index was up 0.11% against a basket of six currencies in the late afternoon trade.
In overseas market, dollar was on the defensive early, nursing deep losses against the euro and yen after Friday's firm US jobs report failed to shift a broadly held view that Federal Reserve will remain cautious on raising interest rates this year.
Oil prices fell in early trading as chances of Middle East producers agreeing to curb over-production appeared to fade, while US output remains stubbornly high.
Pramit Brahmbhatt of Veracity Financial Services said, "The rupee opened at 66.30/dollar weaker compared to previous close of 66.26/dollar thus by appreciating dollar. Following to positive cues from domestic equity market, rupee appreciated and breached the level of 66.20/dollar for the day."
The benchmark index Nifty closed with a gain of 46 points ahead of RBI monetary policy.
Trading range for the spot USD/INR paid is expected to be within 65.80 to 66.50/dollar.
In forward market, premium for dollar moved down on good receivings from exporters.
The benchmark six-month premium for September declined to 206.5-208 paise from 210-212 on last Thursday and far forward March 2017 contract also fell to 403.5-404.5 paise from 407-409 paise.
The RBI fixed the reference rate for the dollar at 66.2430 and euro at 75.3713.
In cross-currency trades, the rupee firmed up further against the pound sterling to finish at 94.36 from 95.50 on last Thursday and also moved up against the euro to 75.26 per euro from 75.40.
However, the rupee dropped against the yen to 59.28 per 100 yen from 59.02 previously.
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