"Ahead of Powell's testimony, investors were seen taking a wait-and-see approach during USA trading overnight, and the Japanese market kept the tone", SMBC Nikko Securities said in a note.
Japan's benchmark Nikkei 225 edged down almost 0.2% to finish at 21,533.48.
The Australian dollar dipped to $0.69190, the lowest in nearly three weeks after Australian consumer sentiment slummed to a two-year low, which could prompt another rate cut from the Reserve Bank of Australia and pressure the government to offer more fiscal support.
Gold prices slipped $3.30 to $1,393.90 U.S.an ounce. Hong Kong's Hang Seng rose 0.5% to 28,248.14, while the Shanghai Composite inched up 0.1% at 2,931.18.
Powell is scheduled to give his semi-annual monetary policy testimony to Congress at 1400 GMT, and investors see a worrying lack of inflation globally as one reason for Powell to sound suitably dovish.
Shares of rate-sensitive lenders, including Goldman Sachs, Bank of America Corp and JPMorgan Chase & Co, fell between 0.2% and 0.7% in premarket trade as yields on the benchmark 10-year U.S. Treasury bond dropped after Powell's comments.
The market rallied through much of June after the central bank signalled it's prepared to cut rates to offset slowing global growth and the fallout from USA trade conflicts.
The second-quarter earnings season starts in earnest next week, but investors are on edge following warnings of the U.S.
Overall growth has also "moderated", the Fed chief said, while "there is a risk that weak inflation will be even more persistent than we now anticipate", and not prove as transitory as Fed officials have often insisted.
Powell's remarks triggered a stock market rally, with the Dow Jones industrial average up almost 200 points in the first half hour of trade. The Dow was up 0.7%, or 188 points, marking its first higher open in four days.
The dollar could continue to creep higher if Powell's comments on the USA economy are perceived as neutral or even slightly hawkish, which would support the argument that additional rate cuts will be limited.
Market expectations have shifted to a smaller interest rate cut than had been expected before the jobs data.
There are also concerns that U.S. President Donald Trump's highly unusual public pressure on the central bank to cut rates sharply could play into the Fed's decision making. He said he would consider a rate cut if the economy weakened substantially, according to The Wall Street Journal.
A lot depends on what Powell says today.
Brent crude futures rose 59 cents to $64.75, while US crude gained 80 cents to $58.63 a barrel. It gained 17 cents to $57.83 a barrel Tuesday. Brent zoomed 61 cents at $64.77, having earlier hit $64.95. The euro has traded between $1.11 and $1.14 since February.