The Indian rupee added losses in opening trades on Tuesday amid firm dollar overseas and muted local equities. Domestic shares opened on a sluggish note Tuesday as concerns prevail over tech valuations and the outlook for U.S. interest rates. Asian markets were deep in the red this morning while gold extended losses for a fourth straight session, weighed down by a firm dollar amid diminished prospects of a Fed rate cut next month. INR opened at Rs 88.67 per dollar and dipped to a low of 88.60 before recovering to 88.66 so far during. Yesterday, rupee pared intraday losses to settle 3 paise higher at 88.63 against the US dollar, tracking firm domestic equity markets and lower global crude oil prices. Benchmark indexes Sensex and Nifty rose around half a percent each on Monday, with underlying sentiment supported by a resounding victory for the BJP-led NDA in the Bihar elections and optimism surrounding a potential India-U.S. trade deal.