The advances came as traders try to ascertain the Federal Reserve's plans for interest rates this year, with focus firmly on the release this week of key inflation data.
The outlook was given a boost by Monday's plunge in oil prices -- a key driver of inflation -- after Saudi Arabian giant Aramco announced a cut of $2 a barrel as it looks to regain lost market share.
Equities have stumbled into the new year as a rally at the end of 2023 came to an end on worries that investors may have been too optimistic that the Fed will slash interest rates as soon as March.
Confidence was given a jolt last week when minutes from the bank's December policy meeting showed decision-makers were happy to keep rates at two-decade highs for some time to make sure they defeat inflation.
That was followed by a forecast-busting jobs report that showed the labour market remained in rude health, reinforcing the Fed view that there was still much work to do before officials could call mission accomplished.
Still, Fed governor Michelle Bowman said rates were at the level needed to bring inflation down to the bank's two percent target.
"Should inflation continue to fall closer to our two percent goal over time, it will eventually become appropriate to begin the process of lowering our policy rate to prevent policy from becoming overly restrictive," she said in prepared remarks at the South Carolina Bankers Association in Columbia.
With eyes on the upcoming consumer price index figures, SPI Asset Management's Stephen Innes said: "If current cooling estimates hold, the month-on-month increase is anticipated to be 0.3 percent, marking the slowest pace of annual core price growth since May 2021.
"This is expected to be perceived positively for risk markets, reinforcing the optimism for market-based rate cuts."
On Wall Street, all three main indexes powered higher, with the Nasdaq up more than two percent.
And Asia picked up the baton, with Tokyo, Hong Kong and Sydney jumping more than one percent, while Shanghai, Seoul, Singapore, Manila and Wellington were also on the rise.
Oil prices edged up slightly but made little headway into the steep Monday losses that came after Aramco's move, which fanned concerns that supply was far outstripping demand, particularly with China's economy still struggling.
The commodity in 2023 suffered its first annual loss since Covid-ravaged 2020 as non-OPEC+ producers filled in for output lost through cuts by Riyadh and other members of the cartel.
Analysts said prices could be even lower if it was not for geopolitical tensions in Ukraine and the Middle East.
Bitcoin was sitting around $46,500, having broken $47,000 on Monday for the first time since April 2022 on bets US regulators will approve exchange-traded funds that invest directly in the cryptocurrency.
- Key figures around 0230 GMT -
Tokyo - Nikkei 225: UP 1.4 percent at 33,858.63 (break)
Hong Kong - Hang Seng Index: UP 1.1 percent at 16,402.12
Shanghai - Composite: UP 0.3 percent at 2,897.34
West Texas Intermediate: UP 0.3 percent at $71.01 per barrel
Brent North Sea Crude: UP 0.5 percent at $76.46 per barrel
Dollar/yen: DOWN at 143.59 yen from 144.19 yen on Monday
Euro/dollar: DOWN at $1.0961 from $1.0963
Pound/dollar: UP at $1.2760 from $1.2740
Euro/pound: DOWN at 85.93 pence from 85.88 pence
New York - Dow: UP 0.6 percent at 37,683.01 (close)
London - FTSE 100: UP 0.1 percent at 7,694.19 (close)
dan/cwl
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