The rupee opened at 52.85 to the dollar, slightly weaker than Friday's close of 52.70/72. It had rebounded last week after hitting a record low of 54.30 on Thursday.
North Korean leader Kim Jong-il died on Saturday, state television reported on Monday.
In the latest in a series of measures to shore up the rupee, the Reserve Bank of India deregulated interest rates on non-resident external rupee deposits and ordinary non-resident accounts.