Mainland Chinese stocks were mixed on the day, with the Shanghai composite up 0.24% to about 2,875.42 while the Shenzhen composite shed 0.427% to approximately 1,800.84. The Hang Seng index in Hong Kong was 0.5%, as of its final hour of trading.
Meanwhile in Australia, the S&P/ASX 200 finished its trading day 1.03% higher at 5,460.50.
Overall, the MSCI Asia ex-Japan index was fractionally higher.
Oil prices rose in the afternoon of Asian trading hours on expectations of demand pick-up and supply cuts. International benchmark Brent crude futures rose 4.34% to $33.91 per barrel. U.S. crude futures also added 5.78% to $31.13 per barrel.
Investors watched for reaction to Powell's recent comments to CBS' "60 Minutes."
"Assuming there's not a second wave of the coronavirus, I think you'll see the economy recover steadily through the second half of the year," the central bank chief said. However, he added that "for the economy to fully recover ... that may have to await the arrival of a vaccine."
"There is no question that the outlook remains grim," Vishnu Varathan, head of economics and strategy at Mizuho Bank, wrote in a note. "US-China friction and the inability to plot a path of recovery from COVID leave much up in the air; and arguably, a little much reliance on policy silver bullets to deliver respite."
On the economic data front, the Japanese economy contracted at an annualized rate of 3.4% between January and March, according to data released Monday by the country's Cabinet Office. That was less than a median estimate of a 4.6% decline by economists in a Reuters poll. Still, the shrinking of the economy marked the country's second straight quarter of contraction, meeting the technical definition of a recession, according to Reuters.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was last at 100.338 after seeing highs around 100.5 last week.
The Japanese yen traded at 107.19 per dollar after strengthening from levels above 107.6 seen early last week. The Australian dollar changed hands at $0.6441 following a decline from levels above $0.65 in the previous week.
— CNBC's Jeff Cox contributed to this report.