The rupee witnessed range-bound trading in initial deals against the US dollar on Thursday, ahead of the Reserve Bank of India's monetary policy outcome. Market participants are awaiting cues from the central bank's observation of recent events and its observations on food inflation which continues to remain high. Foreign fund outflows and gains in Brent crude price further dented investor sentiments. At the interbank foreign exchange, the rupee opened at 83.94 against the greenback, then touched 83.93, registering a rise of 2 paise over its previous closing price. On Wednesday, the rupee consolidated in a narrow range and settled for the day lower by 3 paise at 83.95 against US dollar. "Indian rupee was again sold off as it closed at 83.95 on Wednesday very close to the psychologically important level of 84.00. Market will await the monetary policy before checking on RBI allowing the rupee to fall further as it protects 83.96," said Anil Kumar Bhansali, Head of Treasury and Execu