Traders said good dollar demand from importers including oil companies was seen at stronger rupee levels, limiting any further gains.
The domestic currency resumed higher at 62.30 per dollar as against the last closing level of 62.41 at the Interbank Foreign Exchange Market and firmed up further to 62.20 a dollar.
Most Asian currencies weakened versus the dollar with the Thai baht and Philipine peso sliding on disappointing economic data.
The concessional swap windows have attracted about $25 billion, RBI deputy governor HR Khan said on Monday.
Most immediately, he pledged to move slowly if needed in winding down an oil window that provides dollars directly to state-run oil companies
Iraq is willing to double the credit period on crude sales to 60 days if Indian refiners buy more in 2014, the head of refineries at Hindustan Petroleum said. Iran has also sweetened the deal to expand its dwindling market share by offering free shipment and a nominal discount to Indian refiners, sources said last week.
The previous bout of Fed withdrawal fears had threatened to spark a crisis of confidence in India -- sending the rupee to a record low of 68.85 in late August and leading to steep falls in bonds and stocks.
S&P is the only of the three major credit agencies with a 'negative' outlook on India.
The rupee which has been relatively stable over the last couple of months after having seen as much as 20 percent fall to a record low in late August has been boosted mainly by robust foreign fund inflows into the stock market.
The partially convertible rupee closed at 61.2350/2450 per dollar compared with 61.31/32 on Tuesday.
The RBI's macroeconomic report released after the close of markets said upside risks to food inflation remain and that it expects the retail and wholesale price inflation to remain above comfort levels.
The plan being negotiated by US Senate leaders would end a partial government shutdown and raise the debt ceiling by enough to cover the nation's borrowing needs at least through mid-February 2014, a source familiar with the negotiations told Reuters.
The rupee resumed lower at 61.15 per dollar as against the last weekend's level of 61.07 at the Interbank Foreign Exchange market and hovered in the range of 61.15 and 61.28 before quoting at 61.24 per dollar at 1030 hours.
Sentiments turned buoyant after RBI on Monday cut the marginal standing facility rate, at which it lends emergency funds to banks, by 0.5 per cent to 9 per cent with an aim to improve liquidity and boost economic activities.
Traders say the rupee and other global currencies will likely track the continued uncertainty in the US budget stalemate and government shutdown.
The RBI's comments, announced after trading hours on Wednesday, comes as yields had risen by 60 basis points after a surprise hike in the repo rate on Friday and on worries about the fiscal second borrowing programme of the government.
Oil accounts for about a third of India's total imports and higher dollar prices combined with a rupee near all-time lows have increased its cost.
The partially convertible rupee closed at 63.37/38 per dollar compared with 62.83/84 on Monday. The unit dropped 0.85 per cent on the day, its biggest single-day fall in two weeks.
In the global markets, the US dollar traded lower in early trade after former US Treasury Secretary Larry Summers withdrew himself from the race to be the next Federal Reserve chairman.
The bank says the rupee can reach 57-58 levels though the RBI may try to stem the volatility by starting to build reserves at 60.