The rupee was trading at 81.6850 per dollar by 0520 GMT, up about 0.2% from 81.8450 in the previous session. In contrast, the Korean won, the Thai baht and the Malaysian ringgit rallied between 1% and 1.8%.
The lack of a major response on the rupee to the dollar's fall suggests that it will be a "good idea" to bet on a 81.50-82.00 range for the rupee, a trader at a private sector bank said.
Weak U.S. manufacturing and services data added to the dollar's slump against its major peers, boosting Asian currencies.
U.S. business activity contracted for a fifth straight month in November, with a measure of new orders dropping to its lowest level in 2-1/2 years.
Meanwhile, the Fed's November meeting minutes reinforced expectations that the U.S. central bank will be less aggressive on the rate hike front.
A "substantial majority" of policymakers agreed it would "likely soon be appropriate" to slow the pace of interest rate hikes, the minutes showed. Further, the debate broadened over the implications of the rapid rate hikes.
The Fed has raised rates by 75 basis points (bps) at each of its last four meetings. Futures are now pricing in a high probability that the next hike in December will be a 50-bps one.
Indian shares rose, in line with the rest of Asia. Oil prices were little changed after slipping more than 3% in the previous session. Rupee forward premiums rose.
(Reporting by Nimesh Vora; Editing by Janane Venkatraman)
By Nimesh Vora
