The rupee appreciated 8 paise to 79.61 against the US dollar in opening trade on Friday, tracking the dollar's decline versus its major peers and foreign fund inflows.
At the interbank foreign exchange, the domestic unit opened at 79.66 against the dollar, then touched 79.61 in initial deals, registering a gain of 8 paise over its previous close.
On Thursday, the rupee rose by 26 paise to close at a week's high of 79.69 against the American currency.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.72 per cent to 108.92, as markets digested yet more hawkish Fed.
The US Federal Reserve Chair, Jerome Powell on Thursday said he is "strongly committed" to fighting inflation.
Meanwhile, the European Central Bank raised its key interest rates by an unprecedented 75 basis points.
"ECB raised interest rates by 75 bps, taking the euro higher and the dollar index lower at 109.08 levels. Brent oil remains below $90 per barrel. Asian currencies gain against the dollar," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.
The rupee will stay in a range of 79.40 to 79.80 for the day, Bhansali added.
Brent crude futures, the global oil benchmark, advanced 0.22 per cent to $89.35 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 291.14 points or 0.49 per cent up at 59,979.36. Similarly, the broader NSE Nifty rose 104.65 points or 0.59 per cent to 17,903.40.
Foreign institutional investors (FIIs) were net buyers in the capital markets, as they purchased shares worth ₹2,913.09 crore on Thursday, according to provisional data.