At the close of market hours in India, the dollar index, which measures the greenback's strength against major global currencies, was at 98.843, up one per cent from its previous close.
The rupee was sort of an outlier in Asia, where currencies fell against the dollar.
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The Indonesian rupiyah gained 0.44 per cent against the dollar, but the Chinese renminbi fell 0.59 per cent, the Hong Kong dollar fell 0.02 per cent, the Korean won fell 0.328 per cent, the Singapore dollar fell 0.55 per cent, and the Thai Baht fell 0.40 per cent.
"The Fed rate hike has removed many uncertainties about the course the Fed would take in the coming year. Most of the recent rupee movement was due to panic. Now that is dispelled, it's time the rupee strengthens," said Satyajit Kanjilal, managing director at Forexserve.
Kanjilal expects the rupee to strengthen at 65.50-66 a dollar in the near term. According to India Ratings and Research, a Fitch arm, the rates and currency market will stand to gain in the near term. "The 10-year benchmark G-sec yield likely to soften around the 7.70 per cent mark with bias towards further softening and the Indian rupee will stabilise between 66.3-66.6/dollar during the week. With the Fed's policy normalisation underway, the Reserve Bank of India focus during the upcoming monetary policy reviews will increasingly shift to domestic parameters, critical being the growth-inflation rhetoric," the rater said.