Rajan's announcements have helped sentiments: His appointment has sparked badly-needed optimism among investors, analysts say. Gaurav Kapoor of RBS told NDTV that Dr Rajan has changed the thinking that central bank has a hands off approach to the rupee.

New announcements are credible: Dr Rajan unveiled a slew of proposals to support the rupee and open up markets on Wednesday. The biggest among them was a swap window to banks for new foreign currency nonresident (B) dollar funds, which is expected to lead to an estimated $10 billion of inflows.

Hopes that Rajan will unveil more market-friendly measures were further boosted after the Reserve Bank of India late on Friday made it easier for it for non-residents to buy shares of listed companies.

The government is also set to announce more steps over the next few days to curb non-essential imports, with expectations growing for a hike in subsidised diesel prices that would ease concerns about the government's finances.

Improving global investor sentiment also helped the rupee on Tuesday. Russia's proposal to work with Damascus to put Syria's chemical weapons under international control was seen potentially averting planned U.S. military strikes. Benchmark Brent oil prices fell, extending Monday's slide, a big factor for India since crude oil is its biggest import.

Trade deficit is expected to narrow. Trade secretary S. R. Rao told Reuters on Monday the country's merchandise exports had posted double-digit growth in August, while imports were "contained. The government's steps to curb gold imports has already helped to contain the trade deficit over June and July to a shade over $12 billion, down from a recent monthly average of $17 billion in the earlier six months.

US Fed may delay tapering, or the magnitude of tapering might be less than expected, because of disappointing jobs data. This will help prevent exodus of funds from emerging markets, including India.

Dollar weakness: The dollar weakened against a basket of currencies including the euro, which the rupee tracks closely.

The number of open contracts in domestic rupee futures has slumped in September, which is a sign that traders are removing their short positions in the currency.