Traders began the month on the front foot after a rollercoaster ride since Donald Trump's re-election and warning that he will hit China, Canada and Mexico with hefty tariffs.
They took their cue from New York, where the Dow and S&P 500 both ended at record highs in a holiday-shortened session.
Hong Kong and Shanghai were among the best performers after data showed Chinese manufacturing activity expanded at a faster clip than expected in November.
The purchasing managers index figures provided some hope that the world's number-two economy was turning a corner after a long-running slowdown, with analysts pointing to a raft of support measures unveiled at the end of September.
"The last two months of PMI data offered early signs of green shoots following the recent policy pivot and subsequent stimulus programmes," said Anna Zhou and Helen Qiao at Bank of America Global Research.
"We expect policymakers to step up easing measures next year, including the continuation of the equipment upgrade and consumer goods subsidy programmes, which should help support the manufacturing sector amid deteriorating external demand."
Some commentators also pointed to optimism that Trump could take a more pragmatic approach to tariffs, with Mexican President Claudia Sheinbaum saying after a phone call with the Republican: "There will not be a potential tariff war."
Still, investors were keeping a wary eye on developments as the US president-elect puts his cabinet together.
"Advanced Northeast Asian economies consistently run merchandise trade surpluses with the US," said analysts at Moody's Analytics.
"While falling short of China's $280 billion surplus with the US, or the EU's $207 billion surplus, Japan, South Korea and Taiwan each run surpluses large enough to notice, putting them in the firing line of new tariffs."
There were also gains on Monday in Sydney, Mumbai, Singapore, Taipei, Manila and Bangkok.
Tokyo rose as the yen held recent gains around 150 per dollar, as bets increase on a Bank of Japan interest rate hike after last week's forecast-topping Tokyo inflation report.
BoJ Governor Kazuo Ueda said in an interview with the Nikkei published Sunday that increases were "nearing in the sense that economic data are on track".
Paris stocks shed more than one percent and the euro sat around 14-month lows on concerns about France's budget standoff.
Prime Minister Michel Barnier faces the risk of being deposed by a hostile National Assembly as his government presents a social security financing plan Monday that has the opposition up in arms.
Far-right leader Marine Le Pen said in a Sunday newspaper that her party would not necessarily vote to topple Barnier's government -- so long as he agreed to negotiate.
Le Pen's parliamentary bloc holds the key to the survival of the minority centre-right administration and in an interview with La Tribune Dimanche, she insisted her position was to "remain constructive".
But if Barnier refused to negotiate with her party, he would have taken the "decision to trigger the vote of no confidence" himself, she said.
Shares in London and Frankfurt opened slightly lower.
Key figures around 0810 GMT
Tokyo - Nikkei 225: UP 0.8 percent at 38,513.02 (close)
Hong Kong - Hang Seng Index: UP 0.7 percent at 19,550.29 (close)
Shanghai - Composite: UP 1.1 percent at 3,363.98 (close)
London - FTSE 100: DOWN 0.1 percent at 8,281.22
Dollar/yen: UP at 150.10 yen from 149.60 yen on Friday
Euro/dollar: DOWN at $1.0505 from $1.0580
Pound/dollar: DOWN at $1.2685 from $1.2739
Euro/pound: DOWN at 82.82 from 83.04 pence
West Texas Intermediate: UP 0.9 percent at $68.62 per barrel
Brent North Sea Crude: UP 0.9 percent at $72.48 per barrel
New York - Dow: UP 0.4 percent at 44,910.65 (close)
