The rupee declined by 2 paise to close at 79.80 (provisional) against the US dollar on Tuesday amid a lacklustre trend in domestic equities.

At the interbank foreign exchange market, the domestic currency opened at 79.80 per dollar. It hovered in a range of 79.80 to 79.91 during the session.

The domestic unit finally settled at 79.80, down 2 paise over its previous close of 79.78.

"Rupee traded in a narrow range and volatility was low as most market participants were on the sidelines following the US market holiday," said Gaurang Somaiya, Forex & Bullion Analyst, Motilal Oswal Financial Services.

Somaiya added that the dollar rose to a fresh 20-year high against its major crosses.

"Focus will be on the services PMI number that will be released from the US. Better-than-expected data could extend gains for the greenback. We expect the USD-INR (Spot) to trade sideways and quote in the range of 79.40 and 80.05," Somaiya said.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.10 per cent higher at 109.64.

Brent crude futures, the global oil benchmark, fell by 3.05 per cent to USD 92.82 per barrel.

On the domestic equity market front, the BSE Sensex ended 48.99 points or 0.08 per cent lower at 59,196.99, while the broader NSE Nifty declined 10.20 points or 0.06 per cent to 17,655.60.

Foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 811.75 crore, as per exchange data.