The U.S. dollar drifted higher against its most major counterparts in the Asian session on Wednesday, following comments from Federal Reserve Governor Lael Brainard indicating that the central bank could begin reducing its balance sheet at a rapid pace as soon as May and that an aggressive tightening of monetary policy would be required to control inflation.

The Fed "will continue tightening monetary policy methodically through a series of interest rate increases and by starting to reduce the balance sheet at a rapid pace as soon as our May meeting," Brainard said on Tuesday.

Amid strong recovery, the Fed is expected to trim the balance sheet considerably more rapidly than in the previous recovery, with significantly larger caps and a much shorter period to phase in the maximum caps compared with 2017-19, Brainard added.

Brainard's comments sent the yield on the 10-year treasury note to a multi-year high of 2.567 percent overnight.

The Fed minutes due later today could offer more clues about the pace of rate hikes and balance sheet reduction.

The greenback climbed to 1.3045 against the pound, its strongest level since mid-March. Against the euro, it touched a fresh 4-week high of 1.0874. The greenback is seen finding resistance around 1.28 against the pound and 1.06 against the euro.

The greenback was up against the franc, at an 8-day high of 0.9341. On the upside, 0.95 is seen as its next resistance level. The greenback touched a 2-day high of 1.2510 against the loonie, up from yesterday's close of 1.2482. The greenback may face resistance near the 1.28 level.

In contrast, the U.S. currency retreated from its early highs of 0.7562 against the aussie and 0.6934 against the kiwi and was trading at 0.7593 and 0.6963, respectively. The currency is likely to face support around 0.78 against the aussie and 0.72 against the kiwi.

The greenback held steady against the yen, after having eased from an 8-day high of 124.05 seen at 10:30 pm ET. The pair had closed yesterday's deals at 123.60.

Looking ahead, U.K. construction PMI for March and Eurozone PPI for February are due in the European session.

Canada Ivey PMI for March will be featured in the New York session.

The Fed minutes from the March 15-16 meeting are set for release at 2:00 pm ET.

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