The rupee falls to 53.85/86 from its previous close of 53.80/81 on the back of some dollar short-covering by state-run banks while dollar demand from oil firms also weighed.
The euro slips against the dollar in anticipation of the European Central Bank cutting interest rates in an attempt to support a flagging economy.
Traders say weak manufacturing PMI also boosting dollar sentiment. India's factories lost momentum in April as output grew at its weakest pace in over four years, but a jump in export orders augured well for the coming months, a survey showed on Thursday.
Dealers say the market is sitting short on dollar ahead of the anticipated rate cut on Friday and when the pair fell to a two-month low of 53.6625, some short covering was triggered.