Rupee depreciated 6 paise to 96.42 against the US dollar in early trade on Tuesday pressured by heightened geopolitical tensions, a stronger US dollar and elevated crude oil prices.At the interbank foreign exchange market, the local currency opened at 96.41 and slipped to 96.42, compared with its previous close of 96.36 against the greenback, according to PTI.Forex traders said the rupee remained under pressure as rising geopolitical uncertainty pushed investors towards safe-haven assets, boosting demand for the US dollar. Higher crude oil prices also weighed on the domestic currency by raising concerns over India’s import bill.Meanwhile, the dollar index, which measures the greenback against a basket of six major currencies, was trading 0.03% higher at 100.97. Brent crude, the global oil benchmark, was quoted 0.65% lower at $88.64 per barrel in futures trade.Domestic equities also opened on a weak note. The BSE Sensex fell 58.89 points to 77,649.63, while the NSE Nifty50 declined 22.45 points to 24,216.05 in early trade.Among Sensex stocks, Tech Mahindra, ICICI Bank, Kotak Bank, SBI, Bharti Airtel, Tata Steel, Asian Paints, HCL Tech, TCS, Infosys, Larsen & Toubro and NTPC were among the top gainers, while Eternal, Axis Bank, Maruti, HDFC Bank and Trent were among the major losers.