Nifty and Sensex both hit record highs, after foreign investors on Thursday posted their biggest daily purchases since December 19, amounting to a net 13 billion rupees, and marking a 15th consecutive buying session.
Overseas funds have also become strong buyers of debt, with net purchases of $5.6 billion so far this year.
Analysts attribute the growing foreign confidence in India to the government's success at narrowing the current account deficit by curbing gold imports, as well as to the Reserve Bank of India's action to tame high inflation by raising interest rates.
Still, global uncertainties remain, with tensions lingering in Ukraine. Meanwhile, U.S. monthly jobs data due later in the day could set the tone in global markets by early next week.
"Our view on INR remains tactically constructive as a carry target, as we expected current account conditions to remain supported at least until the government lifts gold restrictions," said Sacha Tihanyi, senior currency strategist at Scotiabank.
"However, we cannot turn structurally bullish on the rupee until inflation and inflation expectations come down significantly," he said.
The partially convertible rupee closed at 61.08/09 per dollar compared with 61.11/12 on Thursday. The unit rose as high as 60.945, its strongest since December 9. For the week, it rose 1.1 percent, its best performance since the week ended Dec 6.
Traders will also be tracking cash conditions given advance tax outflows in mid-March tend to tighten liquidity. Near-term forward premiums spiked on fears of cash tightening and as traders said that a large state-run bank bought to meet oil swap payments.
The 1-month forward premium was last at 52.75 points vs 51 points at Thursday close. It rose to 54.25 points, last seen in early October, as per Reuters data.
A Reuters poll on Friday also cast doubt about whether the rupee can sustain the gains, showing the currency trading at 62 to the dollar in a month, at 63.25 in six months and at 63.60 in a year.
In the offshore non-deliverable forwards, the one-month contract was at 61.41 while the three-month was at 62.09.
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