The comments by Williams made it a virtual certainty the Fed would cut interest rates by 25 basis points at its July 30-31 policy meeting and also fuelled expectations of an even deeper 50 basis point reduction.
Financial markets quickly reacted, with Fed fund rate futures at one point pricing in almost 70 percent chance of a 50 bp cut at the month-end meeting. The odds eased to around 40 percent after the New York Fed clarified that Williams' speech was not about immediate policy direction.
Wall Street shares shook off a sluggish start and moved higher overnight thanks to Williams' dovish comments.
The Shanghai Composite Index and Hong Kong's Hang Seng were both up 1%.
Australian stocks added 0.7%, South Korea's KOSPI rose 1% and Japan's Nikkei advanced 1.65%.
MSCI's broadest index of Asia-Pacific shares outside Japan was up 1%, bouncing back from the previous day's losses.
Over the week, the index has climbed a modest 1%, as riskier assets were partly capped by U.S. President Donald Trump's reiteration of his threat to impose further duties on Chinese imports. The two sides resumed talks recently to seek an end to a year-long trade war that has rattled financial markets and slowed global growth.
"Dovish Fed policy expectations do provide support for the equity markets, which are set to rebound after suffering losses the previous day," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui DS Asset Management. "But factors such as U.S.-China trade issues and tensions over Iran are likely to limit the markets' gains."
The dollar index against a basket of six major currencies stood little changed at 96.787 after losing roughly 0.5% overnight to a two-week low of 96.671 in the wake of comments from the Fed's Williams.
The greenback was up 0.2% at 107.520 yen, crawling away from a three-week trough of 107.210 on Thursday after the New York Fed's clarification of Williams' comments. The currency had previously lost 0.6% against its Japanese peer.
The euro was 0.1% lower at $1.1267 after climbing 0.45% the previous day.
U.S. Treasury yields were lower across the board in light of Williams' dovish views. The 2-year yield was at 1.7826% after touching a two-week low of 1.7520%. The 10-year yield declined to a 10-day trough of 2.023% and was last at 2.0363%.
In commodities, U.S. crude oil futures reversed a large part of the previous day's deep losses, rising 1.8% to $56.34 per barrel.
Crude rallied after the reports the U.S. Navy had destroyed the Iranian drone, clawing back earlier losses during the week. Oil prices had fallen on Thursday amid expectations that crude output would rise in the Gulf of Mexico following last week's hurricane in the region.
Spot gold XAU= extended the previous day's rally made on the prospects of lower U.S. interest rates and brushed a six-year high of $1,452.60 an ounce, before pulling back a touch to $1,443.36. Middle East tensions also helped boost safe-haven gold.
(Editing by Shri Navaratnam and Sam Holmes) ((email@example.com; Reuters Messaging: firstname.lastname@example.org +813-6441-1774))
((To read Reuters Markets and Finance news, click on https://www.reuters.com/finance/markets For the state of play of Asian stock markets please click on: 0#.INDEXA ))