The dollar also strengthened against other currencies in the overseas markets.
The rupee resumed lower at 55.75 a dollar as against last closing level of 55.66 at the Interbank Foreign Exchange (Forex) Market and moved between 55.74 and 55.99 per dollar. It was quoting at 55.91 a dollar at 1040 hrs.
In the New York market, the dollar extended gains against most major rivals such as the euro on Tuesday.
Meanwhile, the BSE 30-stock index, Sensex, was trading down 46.85 points or 0.27 per cent to 17,394.02.
According to Nomura, the rupee might hit 54.5 in the near term owing to global policy stimulus and possible measures from the Reserve Bank of India. It, however, expects depreciation of the currency in the medium term.
It said the rupee could hit even 60 around July-December next year if there is a lack of considerable structural reforms.
(With PTI inputs)