Japan's benchmark Nikkei 225 stocks index closed above 40,000 points for the first time Monday, while oil prices dipped after major crude producers agreed to cut output for a while longer, as expected.
Europe's main stock markets retreated around midday, with London down nearly half-a-percent awaiting a UK pre-election budget Wednesday.
The European Central Bank was Thursday expected to freeze eurozone interest rates as sticky inflation prevents a cut. The week ends with key US jobs data on Friday.
Tokyo is enjoying a record-run higher thanks to Wall Street rallies, robust corporate earnings and optimism over artificial intelligence, analysts said.
Oil was in focus, one day after Russia, Saudi Arabia and several other OPEC+ members announced extensions to oil production cuts first announced in 2023.
The extension to mid-2024 is part of an agreement among oil producers to boost prices following economic uncertainty.
Elsewhere in stock markets trading, Wall Street's S&P 500 and tech-rich Nasdaq ended Friday at all-time highs off continued momentum for AI-linked equities, especially chip-maker Nvidia, which finished with a valuation above $2 trillion for the first time.
Taiwanese chip giant TSMC rose to a record high Monday, gaining 5.2 percent on the global rally in semiconductor stocks, and helped Taipei's Taiex index add nearly two percent.
The solid performance of global markets provides "favourable trade winds for Asian markets as the new week begins", noted Stephen Innes of SPI Asset Management.
While the US Federal Reserve is now expected to begin trimming interest rates later rather than sooner this year, due to recent hotter-than-expected inflation data, markets have been boosted by stellar earnings results from big tech firms in recent weeks.
Investors will be looking this week also to the release of US jobs figures and Fed boss Jerome Powell's testimony to Congress.
"We don't expect the chair to stray very far from the Fed's recent messaging -- officials are in a 'wait-and-see' mode as there's still a lot of ambiguity in the data," said John Briggs, global head of desk strategy at NatWest Markets.
Hong Kong's stock market finished flat Monday and Shanghai closed higher ahead of the start of China's annual legislative conclave, with officials expressing concern over the nation's struggling economy and youth unemployment as they prepare to present policies for the coming year.
While analysts have called for stronger interventions from Beijing to boost the economy, Innes said more measured moves are likely as a "big bang" stimulus could pose long-term risks to stability.
London - FTSE 100: DOWN 0.5 percent at 7,643.21 points
Paris - CAC 40: DOWN 0.1 percent at 7,929.63
Frankfurt - DAX: DOWN 0.2 percent at 17,705.57
EURO STOXX 50: UP 0.1 percent at 4,900.30
Tokyo - Nikkei 225: UP 0.5 percent at 40,109.23 (close)
Hong Kong - Hang Seng Index: FLAT at 16,595.97 (close)
Shanghai - Composite: UP 0.4 percent at 3,039.31 (close)
New York - Dow: UP 0.2 percent at 39,087.38 (close)
Euro/dollar: UP at $1.0857 from $1.0841 on Friday
Dollar/yen: UP at 150.44 yen from 150.11 yen
Pound/dollar: UP at $1.2680 from $1.2656
Brent North Sea Crude: DOWN 0.4 percent at $83.24 per barrel
West Texas Intermediate: DOWN 0.4 percent at $79.63 per barrel
