The rupee inched lower by 6 paise to 78.04 against the US dollar in early trade on Tuesday, as persistent foreign fund outflows and strong dollar demand globally weighed on investor sentiments.

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At the interbank foreign exchange, the rupee opened at 78 against the American dollar, then lost further ground to quote at 78.04, registering a fall of 6 paise over the last close.

On Monday, the rupee appreciated 7 paise to settle at 77.98.

"Continuing FII's outflow and strong dollar demand globally is putting up pressure on Indian Rupee to depreciate further with oil buying for payments," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.

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Global oil benchmark Brent crude futures fell 0.91 per cent to USD 115.17 per barrel.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.36 per cent lower at 104.32.

On the domestic equity market front, the 30-share Sensex was trading 354.27 points or 0.69 per cent higher at 51,952.11, while the broader NSE Nifty advanced 113.80 points or 0.74 per cent to 15,463.95.

Foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 1,217.12 crore, as per stock exchange data.