In Japan, the Nikkei 225 index had risen 0.7 percent by lunchtime, while the broader Topix index had gone up 0.3.
Also, Hong Kong's Hang Seng index is climbing, and had risen 2.1 percent after some hours of trading.
Shenzhen's composite index surged 2.4 percent, while the total in Shanghai climbed 1.1.
Powell opened the door on Friday for a possible cut in the interest rate at the Fed meeting on September 17-18 - and it was received with open arms by Wall Street. When trading closed on Friday, the S&P 500 had risen 1.5 percent, while both Nasdaq's composite index and the Dow Jones industrial index had climbed 1.9 percent.