Mumbai, Oct. 1 -- The Indian rupee traded in a narrow range and fell 3 paise to 95.97 against the US dollar in early trade on Thursday, constrained by ongoing dollar demand from state-run oil companies. However, RBI-backed dollar sales across spot and forward markets continue to cap losses, keeping the exchange rate below the 96.00 threshold. Additionally, sustained foreign portfolio outflows and firm US yields and DXY are keeping pressure on the USD/INR pair. INR opened at Rs 95.95 and slipped to a low of 95.97 so far during the day and as compared to previous close at 95.94. A mixed trend in Asian markets and the overnight weak close on Wall Street led to a weak start for Indian shares on Thursday. Elevated oil prices and bond yields re...