The rupee was just short of the 56 mark as exporters rushed in to sell, pulling the Indian currency down to 55.88/89 but still well below its close of 55.5675/5775 on Monday.
Traders said heavy dollar demand from oil and defence firms and also from some custodian buying by two large foreign banks are hurting the rupee.
Exporters, however, are likely to sell the US currency around 56 levels, preventing a very sharp fall in the Indian currency during this session, traders said.
A fall in other Asian currencies and broad gains in the dollar versus major currencies were also huring the rupee, traders said.