In Asia, MSCI's broadest index of regional shares ended its day up 0.8% and little changed for the week.
Japan's Nikkei gained 1.3%, but was still down 1.9% for the week. Chinese blue-chips gave up on an early rise to end down 0.1% while South Korea's tech-heavy KOSPI rose 1.6% but was still down for a third week running. It also came as the Korean won hit a 14-month high.
Traders are bracing for the U.S. payrolls report ahead of what is likely to be even more closely watched U.S. inflation data next week given the mixed signals that have recently emanated from the Fed.
Thursday's economic data showed activity in the U.S. services sector picked up pace last month with a measure of prices paid jumping to a three-year high. The Fed's "Beige Book" survey also showed economic activity edged up in recent weeks.
After the dovish comments from Waller, Treasuries rallied, led by the short-end, as the yield curve bull steepened on fading bets on imminent rate hikes.
Waller had said that "recent data suggest we are finally seeing some signs of disinflation", and that if it continued, he would be "willing to support holding" rates. In addition, he said he viewed underlying inflation "doing better than the core numbers suggest."
Two-year yields held at 4.33% after falling 5 basis points overnight to move further away from Wednesday's 20-month peak of 4.41%.
Ten-year yields were little changed at 4.75%, having dropped 3 basis points overnight, while 30-year yields were at 5.23% after a 2-basis-point fall overnight. In Europe though, Germany's 10-year Bund yield climbed 0.5 basis points to 3.36%, set for a fourth straight weekly rise and the biggest since mid-July.
Investors in longer-dated bonds remain wary of inflation risks amid few signs of progress between the U.S. and Iran to end their war and reopen the Strait of Hormuz. Oil prices held near six-week highs, with Brent crude futures up 7% this week to $95.52 a barrel.
European natural gas prices have also jumped 7% this week to a three-year high as energy companies grow increasingly anxious about heading into winter with stores at their lowest level for more than a decade.
"Should TTF gas futures push towards 100 in the weeks ahead... the ECB will likely remain on a hiking path," RBC BlueBay Asset Management's Chief Investment Officer Mark Dowding said.
The dollar dropped with lower yields and was fetching 99 against its major peers, after skidding 0.6% overnight. It is set for a weekly drop of 0.7%.
That helped the yen to build on its gains this week as investors ramped up bets on a Bank of Japan rate hike this month. The dollar was last up 0.3% to 156.32 yen, having lost 1.8% overnight.
In commodity markets, gold held at $4,477 an ounce after rallying 2% overnight. It was, however, set to end the week little changed.
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