The Indian rupee traded in a narrow range on Tuesday and depreciated 2 paise to close at 83.97 (provisional) against the American currency, weighed down by the strengthening of the American currency in the overseas market. The US dollar climbed higher to a near one-week high as all eyes turn to a key US inflation data this week that could offer clues on the magnitude of an expected interest rate cut from the Federal Reserve later this month.. The slight recovery in crude oil prices also weighed on the rupee. However, a surge in the domestic markets cushioned the downside. The benchmark S&P/BSE Sensex rose 361.75 points, or 0.44 percent, to 81,921.29 while the broader NSE Nifty index closed at 25,041.10, up 104.70 points, or 0.42 percent, from its previous close. At the interbank foreign exchange market, the local unit opened at 83.95 against the American currency and finally settled at 83.97 (provisional) against the US dollar, down 2 paise from its previous close.