Dealers attributed the rupee's fall to fresh demand for the US currency, but a higher opening in domestic stocks limited the fall.
Major currencies were mostly weak against the dollar overseas after reports that US President Donald Trump would propose tariffs of 25 per cent, instead of 10 per cent, in an announcement that may come as early as today.
Policy meetings of the US Federal Reserve (today) and Bank of England (tomorrow), are also keeping investors cautious; although the US central bank is expected to keep rates unchanged.
Meanwhile, the benchmark BSE Sensex rose 58.95 points, or 0.15 per cent, to hit an all-time high of 37,665.53. NSE Nifty too scaled a new peak high of 11,378.95 in early trade today.