The rupee rose by 19 paise to breach the 80 level against the US currency for the first time in two months on Monday due to a weak dollar in overseas markets.
A fall in crude oil prices and early gains in equity markets also supported the local currency, according to forex dealers.
At the interbank foreign exchange market, the rupee opened higher at 80.92 to a dollar against the previous close of 81.17. The local unit moved in a range of 81.02 to 80.88 in morning deals.
The rupee was trading at 80.98, showing gains of 19 paise over the previous close, at 0930 hrs.
The US dollar index, which gauges the greenback's strength against a basket of six currencies, declined 0.35 per cent to 101.65 amid concerns over US economic growth.
Crude oil prices also declined as traders awaited more clues on Chinese economic recovery and thin Asian trade volumes, analysts said.
The Brent crude declined 0.52 per cent to $87.17 per barrel after a recent rally. The oil for Indian basket also dropped 2.51 per cent to $82.19 per barrel.
On the domestic equity market front, the 30-share BSE Sensex rose by 254.24 points or 0.42 per cent to 60,876.01, while the broader NSE Nifty gained 64.20 points or 0.36 per cent to 18,091.85 in morning trade.
Foreign Institutional Investors (FIIs) were net sellers in the capital market on Friday as they sold shares worth ₹2,002.25 crore, according to exchange data.