At the interbank foreign exchange market, the local unit opened at 83.36 against the greenback. The rupee touched the intra-day peak of 83.35 before trading at 83.36 against the American currency, up 1 paise from its previous close.
On Monday, the domestic currency settled at 83.37 against the US dollar.
"Yesterday, the dollar against its major crosses also traded with low volatility as market participants remain cautious ahead of the important FOMC (Federal Open Market Committee) policy statement that is scheduled to be released later this week,"
He said traders will also keep a tab on the domestic inflation data as well as industrial output numbers to be released later in the day.
"We expect the USD-INR (spot) to trade sideways and quote in the range of 83.20 and 83.50," Somaiya said.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.11 per cent higher at 103.58 on Tuesday.
Brent crude futures, the global oil benchmark, advanced 0.28 per cent to USD 76.24 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 77.50 points or 0.11 per cent higher at 70,006.03 points. The broader NSE Nifty jumped 32.85 points or 0.16 per cent at 21,029.95 points.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Monday as they bought shares worth Rs 1,261.13 crore, according to exchange data.