By Agence France-Presse
Jerome Powell said the US economy was healthy and prices showed no sign of rising more than the bank's two percent target, adding that there appeared to be no risk of overheating.
The remarks at the annual Jackson Hole bankers' symposium in Wyoming on Friday were taken by observers as an indication the Fed will stick to its gradual increases in borrowing costs, which weighed on the dollar but provided a boost to equities.
The S&P 500 and Nasdaq closed at fresh records, while the dollar dropped across the board, with Asian traders extending that trend on Monday.
Tokyo ended the morning 0.7 percent higher, Hong Kong jumped 1.3 percent, Shanghai added 0.8 percent and Singapore put on 0.6 percent. There were also gains in Wellington, Taipei and Jakarta, while Sydney and Seoul were flat.
In forex trading the dollar retreated against its major peers as well as high-yielding currencies, with Mexico's peso boosted by news that US and Mexican officials were close to a deal on a revised free-trade pact.
The yuan also won support after the People's Bank of China said Friday it had made a policy tweak to prevent the currency from falling too sharply.
The central bank adjusted the way it fixes the unit's midpoint each day as it looks to provide more stability at a time when the dollar is broadly in the ascendance.
It also comes as leaders try to temper trade tensions with the United States, with Donald Trump accusing Beijing of keeping the yuan artificially low to boost its exports and offset the impact of tariffs.
The move "should calm both local and international investors that this move does signal the PBoC has no intention of moving into a full-scale currency war in the trade war escalations", said Stephen Innes, head of Asia-Pacific trading at OANDA.
He also said the euro could face headwinds after Italy's populist government threatened to withdraw European Union funding unless it agrees to take some of the 150 people stranded on an Italian coastguard ship.
"I expect the market to start fading on this recent euro move because of Italy's risk, which matters because it's enormous and the ECB is more than content sitting on their hands," Innes said.
Key figures around 0230 GMT
Tokyo - Nikkei 225: UP 0.7 percent at 22,759.53 (break)
Hong Kong - Hang Seng: UP 1.3 percent at 28,018.18
Shanghai - Composite: UP 0.8 percent at 2,750.64
Euro/dollar: UP at $1.1630 from $1.1623 at 2040 GMT Friday
Pound/dollar: UP at $1.2850 from $1.2847
Dollar/yen: UP at 111.23 yen from 111.21 yen
Oil - West Texas Intermediate: DOWN 10 cents at $68.62 per barrel
Oil - Brent Crude: DOWN nine cents at $75.73 per barrel
New York - Dow Jones: UP 0.5 percent at 25,790.35 (close)
London - FTSE 100: UP 0.2 percent at 7,577.49 (close)