Tuesday's closing rate of the rupee against the US dollar was 81.67, up 12 paise as the greenback depreciated from its recent highs.
The local unit against the US dollar started out at 81.72 on the interbank foreign exchange market and fluctuated between an intraday high of 81.64 and a low of 81.83.
On Monday, the rupee depreciated by 5 paise to close at 81.79 against the US dollar.
The rupee was also supported by a recovery in domestic equities and stronger Asian currencies.
The Federal Open Market Committee (FOMC) minutes, which are due Wednesday, will be the focus of immediate attention. It may show consensus on the need to slow hikes but division on the end-point and whether to prioritise inflation or economic growth, he added.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, slipped 0.35 percent to 107.46.
Global oil benchmark Brent crude futures advanced 0.80 percent to USD 88.15 per barrel.
According to exchange data, Foreign Institutional Investors (FIIs) sold shares worth Rs. 1,593.83 crore on Monday, making them net sellers in the capital markets.