The rupee is off lows, slipping to 55.89/90 versus its previous close of 55.42/43 after falling as low as 56.07, the lowest since June 29.
Dealers say some custodian banks are seen selling on behalf of foreign institutional investors.
Euro steadies after earlier hitting a two-year low against the dollar early on Monday, looking vulnerable ahead of a meeting of euro zone finance ministers that will flesh out plans agreed earlier by leaders at a summit late last month.