Forex traders said, however, sustained outflow of foreign funds and an upward movement in crude oil prices put pressure on the local unit and capped its sharp gain.
At the interbank foreign exchange, the rupee opened at 84.39 and slipped further to 84.40 against the greenback, trading 2 paise higher from its previous close.
On Monday, the rupee recovered from its lowest level of 84.46 to settle 4 paise higher at 84.42 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading lower by 0.09 per cent at 106.10.
Brent crude, the global oil benchmark, rose by 0.19 per cent to USD 73.44 per barrel in futures trade.
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