By Agence France-Presse
The broad gains came despite more hefty selling in energy firms after another collapse in oil prices on Friday, while the pound was flat against the dollar after European Union leaders approved a Brexit deal but which must be cleared by British MPs who mostly oppose it.
The positive mood comes at the start of a key week that sees a speech by Federal Reserve boss Jerome Powell and the release of the bank's last policy meeting minutes, before culminating in the G20 in Buenos Aires.
While the summit will focus on several global issues, the meeting between Trump and Xi will get the most attention with the economic superpowers engaged in a trade war just as global growth starts to stutter.
But expectations for a deal to end the standoff are low.
"It would seem that President Xi and President Trump have every incentive to come to an agreement on trade issues, even if that agreement does not significantly change the status quo," said JP Morgan Asset Management chief global strategist David Kelly.
"However, perceptions are important on both sides. While some hold out the hope that an agreement in principle will be reached, it seems more likely that an agreement will have to wait for more posturing on both sides."
Stephen Innes, head of Asia-Pacific trade at OANDA, called the meeting "possibly the best and last opportunity for the two leaders to share middle ground".
"The big question is are we going to see Trump the 'deal maker' or Trump the 'trade warrior' who wants China to 'feel more pain'? Keeping in mind that betting against the latter has been a poor bet for traders this year."
- Crude woes -
Still, the week has started on an upbeat note with Hong Kong jumping 1.5 percent and Shanghai 0.4 percent higher, while Tokyo went into the break 0.8 percent higher.
Singapore added 0.6 percent, Seoul and Taipei each jumped more than one percent, and Manila gained 0.6 percent.
However, Wellington and Sydney both declined.
Oil prices edged up slightly but remain well beaten down after Friday's hammering, which saw WTI sink 7.7 percent and Brent more than six percent, putting them at lows not seen for more than a year.
The commodity has plunged by about a third from its four-year highs touched at the start of October owing to a range of issues, including a global slowdown, the trade row, rising supplies, softer-than-expected US sanctions on Iran, a stuttering China and strong dollar.
The retreat comes ahead of a meeting of the Organization of the Petroleum Exporting Countries on December 6.
"At the root of the oil market woes, there is too much supply and too little demand," said Innes. "But much of the near term price recovery will be driven by what happens in G20 in Buenos Aires and at the OPEC summit in Vienna a week later."
The losses in crude prices have battered energy firms over the past two months, and they continued to fall Monday.
Hong Kong-listed PetroChina fell 1.5 percent, while Sinopec was one percent off. Inpex dropped 2.9 percent in Tokyo and Woodside Petroleum sank 2.2 percent in Sydney.
On currency markets, the pound was barely moved against the dollar as British Prime Minister Theresa May faces an uphill struggle pushing through her draft Brexit deal, with MPs on both sides against it.
May has staked her political future on the agreement and failure would likely lead to the toppling of her government, fuelling fresh uncertainty and hitting the sterling.
EU leaders have said the deal is the best possible one Britain could hope for, meaning a rejection of it will more than likely see the country crash out of the bloc.
Key figures around 0230 GMT
Tokyo - Nikkei 225: UP 0.8 percent at 21,815.55 (break)
Hong Kong - Hang Seng: UP 1.5 percent at 26,314.63
Shanghai - Composite: UP 0.4 percent at 2,590.89
Pound/dollar: UP at $1.2810 from $1.2805 at 1930 GMT Friday
Euro/dollar: UP at $1.1333 from $1.1331
Dollar/yen: UP at 113.07 yen from 112.85 yen
Oil - West Texas Intermediate: UP 40 cents at $50.82 per barrel
Oil - Brent Crude: UP 67 cents at $59.47 per barrel
New York - Dow Jones: DOWN 0.7 percent at 24,285.95 (close)
London - FTSE 100: DOWN 0.1 percent at 6,952.86 (close)