"Rupee has been trading in a range and will continue to do so. With Sensex hitting life-time high, it gives a psychological comfort that (FII) flows are continuing and will continue."
The currency is likely to trade between 64.25 and 64.75 during the week, First Rand Bank head of treasury Harihar Krishnamurthy said.
On Friday, the Sensex crossed the 31,000 mark for the first time ever, ending at 31,028.21, up 278.18 points, or 0.90 per cent.
The broader Nifty index breached the 9,600 level, also in a first, before settling at a record high of 9,595.10.
"Globally, India is perceived as a high growth economy and so FIIs are flocking here. Rupee will continue to gain," said a senior treasury dealer with a state-run bank. He sees the rupee rising to 64.10 this week, triggering some buying from oil companies and RBI at that level, which will lead to depreciation of the domestic currency.
"Recent rise in the stock market in mainly on account of domestic institutional investors and it has not supported much to the rupee's gain. Higher demand for dollars towards the end of the month will put pressure on the rupee this week. It will trade in 64.40-64.80 range," said a treasury officer
at a private-sector bank.
On Friday, overseas investors pumped in Rs 789.20 crore into equity markets but sold Rs 206.71 crore in the debt market.
In the month of May so far, FPIs have invested Rs 24,775.99 crore on a net basis, with Rs 9,006.88 crore in equities and Rs 15,769.11 crore in the debt market.