The weakness in rupee continued for the fourth straight day due to month-end dollar demand by importers.
At 9:30am, the rupee was trading at 62.80 compared with previous close of Rs 62.77 per dollar.
Currency dealers anticipate further weakening of the rupee against the dollar during this week and say it may breach Rs 63 per dollar.
However, there are also hopes that the Reserve Bank of India (RBI) will intervene through state-run banks and not allow the rupee to weaken significantly.