Chinese markets erased earlier gains to close lower: The Shanghai composite was down 0.14 percent to close at around 2,575.81 while the Shenzhen composite slipped 0.316 percent to 1,330.92.
Hong Kong's Hang Seng index gained 1.62 percent in late-afternoon trade.
Investors are looking ahead at a highly anticipated meeting between President Xi Jinping and President Donald Trump at the upcoming G-20 summit in Buenos Aires, Argentina, which is scheduled to happen at the end of this week.
"I think at the moment both China and America are being hurt by this trade war," David Kuo, CEO of The Motley Fool Singapore, told CNBC's "Street Signs" on Monday.
"There is no denying that," he said. "I think this G-20 they'll sit down and they'll have a discussion and they'll go: 'Let's cool it off for a bit.'"
Elsewhere, Japan's Nikkei 225 rose 0.76 percent to close at 21,812 while the Topix index saw gains of 0.2 percent to 1,632.20. South Korea's Kospi advanced 1.24 percent to 2,083.02.
Over in Australia, the benchmark ASX 200 fell 0.78 percent to 5,671.60, with the energy subindex down 2.46 percent and the materials sector off by 2.47 percent.
Major miners declined: Shares of Rio Tinto fell 3.56 percent while Fortescue Metals Group declined 3.99 percent. BHP Billiton dropped 3.55 percent. Metal prices fell on Friday amid concerns over weaker demand from China.
Oil prices recover after Friday loss
U.S. benchmark West Texas Intermediate crude ended Friday's session down $4.21, or 7.7 percent, at $50.42. WTI hit its weakest price since mid-October 2017 on Friday.
International benchmark Brent crude dropped $3.66, or 5.9 percent, to $58.94 by 1:34 p.m. ET. The contract hit its lowest level since late October 2017.
Friday's declines further ramp up the pressure on OPEC ahead of a much-anticipated meeting between the influential oil cartel and its allies in Vienna on Dec. 6, when they are expected to announce that output will be curtailed.
"OPEC should cut production, probably at least a million barrels," Dominic Schnider, head of commodities and Asia-Pacific foreign exchange at UBS Wealth Management, told CNBC on Monday. "I think that's going to see prices actually going up quite sharply."
However, Schnider warned that the market could be "underpricing the fact the we are losing barrels" as a result of recent events such as the reimposition of U.S. sanctions on Iranian crude exports.
"Maybe in the short-term, we have enough supply but I think going into 2019, the market will tighten up," he said.
On Monday afternoon, U.S. crude futures gained 1.45 percent at $51.15 per barrel while Brent was up 2.04 percent at $60 per barrel.
The slight recovery in oil prices failed to boost energy stocks in the region. Australia's Santos fell 4.69 percent, Oil Search was down 4.03 percent, Woodside Petroleum declined 2.27 percent while Beach Energy dropped 3.93 percent.
Over in Japan, Inpex fell 2.44 percent while JXTG dropped 2.26 percent and Japan Petroleum Exploration saw losses of 2.70 percent. Fuji Oil, on the other hand, rose 1.60 percent. South Korea's S-Oil fell 3.21 percent while SK Innovation declined 1.75 percent.
The losses extended to China, where shares of PetroChina fell 0.52 percent and China Petroleum & Chemical, also known as Sinopec, slipped 0.86 percent.
EU leaders back Brexit deal
European Commission President Jean-Claude Juncker reiterated his sadness at the U.K.'s departure, telling reporters in the Belgian capital that it was a "tragedy." But he backed May's plan and said it was the best deal possible for Britain.
But the EU's acceptance of the deal has enraged some pro-Brexit politicians in the U.K. who believe that May is making too many concessions to the EU. May faces a tough challenge next month when she needs to gain Parliamentary approval for the deal in Westminster. The vote — likely to be on December 11 — is crucial for May to move forward with Brexit and failure could lead to her being toppled as leader or even the U.K. crashing out of the EU without a deal.
The British pound traded at $1.2822 on Monday afternoon after seeing an earlier low of $1.2794.
The Japanese yen was at 113.21 against the dollar after seeing an earlier high of 112.85. The Australian dollar traded at $0.7259 after climbing from a low of $0.7220.
— CNBC's Matt Clinch, Sam Meredith and Tom DiChristopher contributed to this report.