Maintaining its strong upbeat trend, the rupee resumed higher at 66.81 from the overnight close of 66.85 on sustained dollar unwinding. But it soon fell to hit a low of 66.99 briefly before regaining momentum, which took the currency to an intra-day high of 66.77.
The recovery was short-lived as intense volatility pulled back the local unit to end the day lower at 66.88, a loss of 3 paise, or 0.04 per cent.
The greenback staged a smart rebound after Trump promised tax reforms within weeks.
Market sentiment also turned cautious ahead of key macro data in the day -- industrial production (IIP) for December.
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Expectations of robust capital inflows, however, capped losses in the rupee, a dealer said.
The US dollar index was trading higher at 100.80 in the late afternoon session.
RBI fixed the reference rate for the dollar at 66.9367 and for the euro at 71.3344.
In cross-currency trade, the rupee recovered against the British pound to close at 83.53 from 83.88.
However, the home unit hardened further against the euro to end at 71.16 from 71.39 and also surged against the Japanese yen to end at 58.95 per 100 yens from 59.45 earlier.