The rupee started the session on a flat note against the U.S. dollar on July 13 amid a rally in the equity markets and easing retail inflation.
A strong greenback against major currencies and foreign capital outflows kept investors cautious in early trading, forex dealers said.
At the interbank foreign exchange, the rupee opened strong at 79.55 against the American dollar, then turned volatile to trade in a tight range of 79.53 to 79.60. The domestic unit was trading at 79.58 against the greenback in early deals, registering a gain of just 1 paisa over the last close.
In the previous session, the rupee had closed at an all-time low of 79.59 against the greenback.
On the domestic equity front, the 30-share Sensex was trading 206.14 points or 0.38% higher at 54,092.75, while the broader NSE Nifty rose 61.65 points or 0.3% to 16,119.95.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, gained 0.12% to 108.20.
Global oil benchmark Brent crude futures rose 0.29% to $99.78 per barrel.
Retail inflation eased slightly to 7.01% in June but was above the central bank's tolerance band for the sixth month in a row, signalling more interest rate hikes in future. Retail inflation in May was 7.04%, government data released on Tuesday showed.
Foreign institutional investors remained net sellers in the capital market on Tuesday, offloading shares worth ₹1,565.68 crore, as per exchange data.
Factory output growth strengthened to a 12-month high of 19.6% in May from 6.7% in the previous month.
With consumer price index based inflation remaining high, Finance Minister Nirmala Sitharaman on Tuesday said the government is watchful of the price situation and will continue the pointed attack on inflation.
