The rupee rebounded by 34 paise to close at a month high against the US dollar on Friday amid domestic equity indices surging to record high levels and losses in crude oil prices.

FII inflows into local equities and the greenback trading near one-month low levels also bolstered the rupee sentiment, analysts said.

At the interbank foreign exchange, the domestic unit opened higher at 81.97 and moved in a range of 82.02 to 81.86 in the day trade.

The unit settled at 81.94 against the US dollar, reflecting gains of 31 paise over the previous close.

On Thursday, the rupee settled lower at 82.25 against the dollar due to a strong greenback overseas and a negative trend in domestic equities.

Crude oil prices were trading lower on Friday with the benchmark Brent crude slipping 0.58 per cent to USD 75.23 per barrel.

The dollar index, which gauges the greenback's strength against a basket of six currencies, was marginally up 0.08 per cent at 102.20.

In the domestic equity market, the 30-share BSE Sensex rallied 466.95 points to settle at a lifetime high of 63,384.58, while broader NSE Nifty climbed 137.90 points to close at a record 18,826.

Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Thursday as they purchased shares worth Rs 3,085.51 crore, according to exchange data.

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