The decline in dollar comes after Powell, on Friday, told the American Economic Association that the Fed is not on a preset path of interest rate hikes and that it will be sensitive to the downside risks the markets are pricing in.
Japan's Nikkei shot up 3.1 percent, helped in part by a pullback in the yen, while South Korea added 1.5 percent.
A USA delegation is in Beijing for trade talks with Chinese officials, the first face-to-face encounter since Trump and Xi agreed to a temporary truce on december 1.Wednesday sees the release of minutes from the Fed's december 18-19 policy meeting.
"The Fed is listening to the market and has acknowledged flashing market signs", said Sim Moh Siong, currency strategist at Bank of Singapore.
Silver was steady at $15.69 per ounce, while platinum fell 0.7 percent to $816.71, having touched a more than one-month high of $831.10 earlier in the session.
Financial markets have been rattled by heightened worries about slowing global growth, especially in the United States and China, though data on Friday showed strong USA job growth.
The US dollar had gained 4.3 per cent in 2018 as the Fed hiked rates four times on the back of a strong domestic economy, falling unemployment and rising wage pressures.
Markets had already gone much further to price in a major chance of a cut in rates this year, and some of that exuberance was tempered by Powell's emphasis on the word "patient" in his speech on Friday.
The Federal Reserve may only need to raise interest rates once in 2019, Atlanta Fed President Raphael Bostic said on Monday, focusing on business executives' nervousness about the economy and a global slowdown as factors that may hold the U.S. central bank back.
Global foreign exchange market embraced the first day of the week with bumpy trading as fewer interest rate hikes later would lead to more hot money flowing in the market.
Chinese stocks firmed after the country's central bank announced an easing in policy on Friday, with 100 basis points of cuts to bank reserve requirements freeing up around $116 billion for new lending.
A further step by China's central bank late Friday to secure liquidity to the slowing economy may also help assuage concerns.
Goldman Sachs researchers expect a bounce in equity markets in 2019.
However, with global stocks largely staying higher amid renewed optimism about a U.S.
European stocks were more or less flat across the board, though mining stocks surged 1.1 percent after the reserve requirement ratio cut from China boosted metals prices, especially steel and iron ore. USA gold futures eased slightly at $1,288 per ounce.
The two sides have until March 1 to make a deal, after which Trump has pledged to ramp up tariffs to 25 percent, from 10 percent, on $200 billion worth of Chinese imports.
Spot gold was up about 0.6 percent at $1,292.41 per ounce as of 1254 GMT.
Commodity currencies such as the Canadian dollar gained 0.1 percent versus the greenback at C$1.3361 due to a rebound in oil prices.