The central bank is also stepping-in to buy dollars when the rupee strengthens, further capping gains. Data late on Friday showed India's foreign exchange reserves rose to $317.85 billion as of July 18, the highest since October 2011.
Traders expect the rupee to remain in a narrow range, unless global events flare up.
This week analysts will look for US-focused action, including the two-day Federal Reserve meeting ending on Wednesday and non-farm payrolls figures on Friday.
"We expect the pair to remain in a very narrow range for the near term as all
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