The rupee slipped 2 paise to an all-time low of 84.40 against the US dollar in early trade on Tuesday, as persistent foreign fund outflows and strength of the American currency in the overseas market dented investors' sentiments.

Forex traders said the rupee is expected to trade between 83.80 and 84.50 in the medium term with the Reserve Bank of India likely limiting any significant downside, aided by its robust foreign exchange reserves.

At the interbank foreign exchange, the rupee opened at 84.39 against the greenback, then fell further to an all-time low of 84.40, registering a fall of 2 paise over its previous close.

On Monday, the rupee dropped 1 paisa to hit a new lifetime low of 84.38 against the US dollar, registering the fourth straight session of loss.

"The Reserve Bank of India plays a key role in stabilizing the rupee, curbing its depreciation. Despite the Emerging Market Currencies Index dropping 6.30 per cent from October 2, the rupee fell only 0.69 per cent, reflecting the RBI's strong defence of the currency," CR Forex Advisors MD Amit Pabari said.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading higher by 0.09 per cent at 105.63.

Brent crude, the global oil benchmark, fell 0.25 per cent to USD 71.65 per barrel in futures trade.

On the domestic equity market front, Sensex was trading 77.35 points, or 0.02 per cent higher, to 79,573.50 points. The Nifty rose 19.90 points, or 0.08 per cent, to 24,161.20 points.

Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday, as they offloaded shares worth Rs 2,306.88 crore, according to exchange data.

"Foreign investments in Indian equities have sharply declined, with over USD 2 billion withdrawn in November following an USD 11 billion outflow in October. This trend reflects overvalued Indian stocks and weak Q2 earnings, dampening foreign capital interest," Pabari said.

Meanwhile, an SBI research report on Monday said that the rupee may depreciate 8-10 per cent against the US dollar during the Trump 2.0 regime.

The report, titled US Presidential Election 2024: How Trump 2.0 Impacts India’s and Global Economy, emphasised that the rupee can have a brief spell of depreciation against the US dollar, followed by appreciation.

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