According to forex dealers, the greenback is currently trading at 166.55 against the domestic currency at the interbank foreign exchange market.
The dollar had finished at Rs166.76 against the local unit the other day.
The dollar fell against most currencies on Thursday as a rally in riskier assets such as global equities and commodities put a dent in safe-haven demand for the US currency.
China’s yuan rose to a four-month high against the greenback.
The euro could get a further boost later in the day as Germany is scheduled to release export data. Economists expect shipments from the euro zone’s largest economy to rebound sharply in May from a large decline in the previous month.
The greenback also fell to a three-week low against the pound GBP= at $1.2637.
Sterling edged up to 89.97 pence per euro EURGBP=D3.
The dollar fell to a four-month low of 0.9365 Swiss franc CHF= on Thursday.
The dollar was little changed at 107.27 yen JPY.