The rupee gained 4 paise to 81.87 against the US dollar in early trade on Tuesday supported by a bullish trend in domestic markets and steady foreign fund inflows.

However, a strong US dollar and surge in crude oil prices capped sharp gains for the local unit, forex traders said.

At the interbank foreign exchange, the domestic unit opened at 81.90 against the dollar and then rose to 81.87, registering a gain of 4 paise over its previous close, as benchmark indices touched all-time highs.

In initial trade, the rupee also touched a low of 81.95 against the American currency.

On Monday, the rupee closed at 81.91 against the US currency.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.03 per cent to 103.01.

Brent crude futures, the global oil benchmark, advanced 0.63 per cent to USD 75.12 per barrel.

Traders further said the rupee's direction will likely be influenced by the release of the Federal Open Market Committee (FOMC) meeting minutes on Wednesday.

"Given the resilience in the labour and housing market coupled with growth would keep the Fed on its intended path of hiking despite changing market opinions after each data release," CR Forex Advisors MD-Amit Pabari said.

Pabari further said the DXY would remain supported around 102 levels. The US markets are closed on Tuesday on account of independence day, and volatility would likely be muted across.

In the domestic equity market, the benchmark indices touched all-time high levels. The 30-share BSE Sensex advanced 176.73 points or 0.27 per cent to 65,381.78. The broader NSE Nifty rose 32.90 points or 0.17 per cent to 19,355.45.

Foreign Institutional Investors (FIIs) were net buyers in the capital market on Monday as they purchased shares worth Rs 1,995.92 crore, according to exchange data.

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