The rupee depreciated 7 paise to 95.68 against the US dollar in early trade on Tuesday, weighed down by elevated crude oil prices and persistent demand for greenback.

Forex traders said Brent crude near $91 per barrel increased oil-related dollar demand and the Reserve Bank's earlier-than-expected closure of the concessional FCN (B) forex-swap facility raised concerns over future dollar inflows.

At the interbank foreign exchange, the rupee opened at 95.68, down 7 paise from its previous close. On Monday, the rupee depreciated 19 paise to close at 95.61 against the US dollar.

The rupee opened lower as oil prices rose with the US and Iran remaining at odds over the Strait of Hormuz and there was no progress on a peace deal, Anil Kumar Bhansali, Head of Treasury and Executive Director, Finrex Treasury Advisors LLP, said.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading at 99.63, down 0.01 per cent.

Brent crude, the global oil benchmark, was trading higher by 0.52 per cent at $91.34 per barrel in futures trade.

"Rupee looks vulnerable to the rising oil prices which have remained close to $90 and have now risen above $91 per barrel. RBI was protecting near 95.61 on Monday and may be protecting 95.75 today but will allow the depreciation to continue in view of the rising oil prices and consistent demand from oil companies," Bhansali said.

On the domestic equity market front, Sensex was trading down 278.32 points to 77,450.64 in early trade; while the Nifty fell 57.65 points to 24,230.45.

Foreign institutional investors offloaded equities worth ₹2,535.10 crore on a net basis on Monday, according to exchange data.