The Indian rupee moved in a narrow range before settling flat at 83.73 (provisional) against US dollar on Monday as a firm American currency in overseas markets offset the gains from weak crude oil prices. A recovery in the US dollar and dollar demand from importers restricted gains for the domestic unit. At the interbank foreign exchange market, the local unit opened at 83.70 and touched a low of 83.74 against the dollar during the trading session. Meanwhile, Indian shares ended a choppy session little changed on Monday as signs of escalating tensions in the Middle East offset hopes for more interest rate cuts from the Federal Reserve this year. The benchmark S&P BSE Sensex hit a new high of 81,908 in intra-day trades before ending the session up 23 points at 81,355. The broader NSE Nifty index reached a new high at 24,999 before settling marginally higher at 24,836.