The advances come even as central bank officials try to push back against expectations, which have set markets up for a healthy end-of-year rally.
The next key event this week will be the release of the US personal consumption expenditures (PCE) price index, which is the Fed's preferred gauge of inflation.
The reading's fall in recent months, along with consumer prices and a slowing jobs market, has been among the main reasons decision-makers are feeling confident that they are on the right track.
Still, they are trying to prevent investors getting ahead of themselves by tempering expectations.
The latest was Atlanta Fed boss Raphael Bostic, who said: "For me, I'm thinking inflation is going to come down relatively slowly in the next six months, which means there's not going to be urgency for us to pull off our restrictive stance."
That comment came after Chicago Fed chief Austan Goolsbee said he was confused by the strong market reaction and New York Fed chief John Williams said traders were being premature.
Still, Wall Street enjoyed another strong day, with the Dow finishing at a fifth straight record high, while the S&P 500 approached its own all-time peak.
Asia was happy to pick up on the positive vibes.
Tokyo and Seoul rose more than one percent, while there were also healthy gains in Hong Kong, Mumbai, Sydney, Bangkok, Singapore, Taipei, Manila and Jakarta, though Shanghai and Wellington sank.
"Financial markets are currently basking in anticipation of a more festive holiday season, revelling in the optimism of profitable Santa Rally cheer," said SPI Asset Management's Stephen Innes.
"Indeed, The Federal Reserve seems ready to offer relief in the coming year, signalling the likelihood of at least three rate reductions in 2024."
The yen struggled to recover after tumbling Tuesday in response to the Bank of Japan's decision not to shift from its ultra-loose monetary policy and to give no guidance for the new year.
The dollar remained under pressure against sterling and the euro as the Bank of England and European Central Bank have been less dovish in their rate outlooks.
And oil prices ticked higher following a rally over the previous two days fuelled by companies suspending transit via the Red Sea owing to attacks on cargo ships by Yemen's Iran-backed Huthi rebels in solidarity with Gaza.
- Key figures around 0700 GMT -
Tokyo - Nikkei 225: UP 1.4 percent at 33,675.94 (close)
Hong Kong - Hang Seng Index: UP 0.5 percent at 16,590.12
Shanghai - Composite: DOWN 1.0 percent at 2,902.11 (close)
Dollar/yen: UP at 143.93 yen from 143.89 yen on Tuesday
Euro/dollar: DOWN at $1.0959 from $1.0979
Pound/dollar: DOWN at $1.2716 from $1.2727
Euro/pound: DOWN at 86.13 pence from 86.25 pence
West Texas Intermediate: UP 0.2 percent at $74.09 per barrel
Brent North Sea crude: UP 0.1 percent at $79.32 per barrel
New York - Dow: UP 0.7 percent at 37,557.92 (close)
London - FTSE 100: UP 0.3 percent at 7,638.03 (close)
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