Rupee trading at 62.18/19 versus its close of 62.44/45 on Wednesday and close to the day's high of 62.1225.
Traders say gains in the domestic share market also helping sentiment. The Sensex was trading up 0.5 percent.
The Reserve Bank of India late on Wednesday relaxed the minimum maturity tenure for banks' foreign currency borrowings' to one year from three years, in order to use the central bank's swap facility which was set up to support the ailing rupee.
Most Asian currencies also stronger compared to the dollar. See for a snapshot.