At the Interbank Foreign Exchange, the rupee opened weak at 71.01 then fell to 71.02 against the US dollar
The 30-share BSE index was trading 24.89 points or 0.06 per cent lower at 41,533.68.
The 30-share BSE Sensex settled 206.40 points, or 0.50 per cent, higher at its all-time closing high of 41,558.57.
On the Sensex, metal stocks drove the rally riding on US-China trade deal optimism.
Forex traders said muted opening of domestic equities weighed on the rupee.
BSE Sensex closed 413.45 points, or 1.01 per cent, higher at its all-time high of 41,352.17.
I think Uday (Kotak) is the best candidate to acquire Yes bank. You need deep pockets, Uday has that, said SBI's Rajnish Kumar.
Forex traders said market participants were enthused following positive developments on the US-China trade talk front.
The 30-share Sensex rose 203.40 points or 0.50 per cent to 41,142.12 in morning session.
The delays to pass on the money are due to a slip in collections and the states have nothing to worry, said FM Nirmala Sitharaman.