With several markets still closed for the Easter holiday, business was limited ahead of a week that will see the release of key data that should give an insight into the impact of the US president's trade war.
Several nations have moved to cut a deal with Washington to stem the worst of the White House's levies, with Japan the highest profile economy.
However, China warned governments on Monday not to seek an agreement that compromised Beijing's interests.
While the rest of the world has been slapped with a blanket 10 percent tariff, China faces levies of up to 145 percent on many products. Beijing has responded with duties of 125 percent on US goods.
"Appeasement will not bring peace, and compromise will not be respected," a commerce ministry spokesperson said in a statement.
"To seek one's own temporary selfish interests at the expense of others' interests is to seek the skin of a tiger," Beijing said.
That approach, it warned, "will ultimately fail on both ends and harm others".
The remarks come after Trump said Thursday that the United States was in talks with China on tariffs, adding that he was confident the world's largest economies could make a deal to end the bitter trade war.
"Yeah, we're talking to China," he said. "I would say they have reached out a number of times."
"I think we're going to make a very good deal with China."
Concerns about the global economic outlook pushed safe haven assets higher, with gold hitting a new record high above $3,384.
The precious metal was also helped by a weaker dollar, which has also been hit by worries about Trump's standoff with Fed boss Jerome Powell.
The president raised worries about the bank's independence when he last week lashed Powell for warning that the tariffs were "highly likely to generate at least a temporary rise in inflation" and suggested interest rate cuts were unlikely.
Trump later called on him to slash borrowing costs and added: "If I want him out, he'll be out of there real fast, believe me."
Powell has said he had no plans to step down early, adding that he considered the bank's independence over monetary policy to be a "matter of law".
The dollar fell against its main peers, with the yen and euro among the best performers.
French Finance Minister Eric Lombard said: "Donald Trump has hurt the credibility of the dollar with his aggressive moves on tariffs -- for a long time."
If Powell is pushed out "this credibility will be harmed even more, with developments in the bond market", he told La Tribune Dimanche newspaper.
Chicago Fed boss Austan Goolsbee on Sunday told CBS's Face The Nation: "There's virtual unanimity among economists that monetary independence from political interference -- that the Fed or any central bank be able to do the job that it needs to do -- is really important."
Stocks had a mixed start to the week, with Tokyo weighed by the stronger yen and Taipei also in negative territory. But Shanghai, Seoul, Singapore, Manila and Jakarta rose.
Oil prices dropped on demand fears as worries about the global economy swirl.
Traders are keeping tabs on the release of key April manufacturing data around the world this week, hoping for an idea about the early impact of Trump's tariffs.
"One thing that's absolutely clear -- and no longer debatable -- is that the reputational hit to the US brand is real, and it's not fading quietly into the next news cycle," said Stephen Innes at SPI Asset Management.
"It's sticking. Investors, allies, and even central banks are starting to bake in the idea that American policymaking, both fiscal and monetary, is now a geopolitical variable -- not a given," he added.
- Key figures at 0230 GMT -
Tokyo - Nikkei 225: DOWN 1.2 percent at 34,300.35 (break)
Shanghai - Composite: UP 0.5 percent at 3,292.98
Hong Kong - Hang Seng Index: Closed for a holiday
Euro/dollar: UP at $1.1476 from $1.1371 on Thursday
Pound/dollar: UP $1.3353 at $1.3270
Dollar/yen: DOWN at 141.03 yen from 142.33 yen
Euro/pound: UP at 85.94 pence from 85.68 pence
West Texas Intermediate: DOWN 1.7 percent at $62.91 per barrel
Brent North Sea Crude: DOWN 1.7 percent at $66.84 per barrel
London - FTSE 100: Closed for a holiday
New York - Dow: Closed for a holiday
dan/mtp
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