At the interbank foreign exchange market, the local unit moved in a narrow range. It opened at 83.95 against the American currency and touched 83.98 in initial trade, registering a fall of 3 paise over its previous close.
On Monday, the rupee traded in a narrow range and closed flat at 83.95 against the American currency.
The US dollar was steady in early trading on Tuesday, with yen inching lower to 143.37 as investors braced for the US CPI inflation for further cues.
"Market would keep a close watch on the Reserve Bank of India (RBI) which may continue selling US dollars to protect the rupee from crossing 84.00," Anil Kumar Bhansali, Head of Treasury and Executive Director Finrex Treasury Advisors LLP.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was up 0.08 per cent to 101.63 points.
Brent crude, the international benchmark, was trading lower by 0.07 per cent to USD 71.79 per barrel in futures trade.
In the domestic equity market, the 30-share BSE Sensex advanced 10.11 points, or 0.01 per cent, to 81,569.65 points, while the Nifty was up 10.05 points, or 0.04 per cent, to 24,946.45 points.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Monday, as they purchased shares worth INR 1,176.55 crore, according to exchange data.
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