The partially convertible rupee rose to as much as 60.83 per dollar, its highest since August 12.
It was last trading at 60.84/85 per dollar, compared with its close of 61.08/09 on Friday.
The BSE Sensex closed marginally stronger after earlier posting its third consecutive record high as strong foreign buying continued to boost domestic-focused shares such as HDFC Bank.
Foreign funds have bought $852.10 million in equities and $5.6 billion in debt so far in this calendar year.
Image: A shopkeeper counts currency notes; Photograph: Reuters
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