Most investors are moving cautiously also ahead of the G20 summit next week where US President Donald Trump and his Chinese counterpart Xi Jinping are due to hold hotly-awaited talks on their long-running trade war.
Hong Kong stocks rallied Monday however, leading many Asian markets higher after last week's losses, with investors cheering a decision by the city to suspend plans to push through a controversial extradition law.
In a separate development, Britain and China on Monday began selling shares in each others' companies under a landmark deal, as London looks to remain a leading financial centre post-Brexit.
The launch of the London-Shanghai Stock Connect marks "the first time that any foreign company will be able to list in mainland China", a statement said, as the UK seeks to extend close trading ties with the Asian powerhouse, despite strains caused by the Huawei fallout.
"During the week, the focus is going to remain on central banks and their monetary policies," said anlayst Naeem Aslam at London-based trading firm ThinkMarkets.
"Traders are betting that the Federal Reserve will take a U-turn this year for its monetary policy and it is only a matter of time before we see a rate cut by the Fed."
The US central bank will unveil its monetary policy announcement on Wednesday, followed by both the Bank of Japan and the Bank of England on Thursday.
Many observers are tipping a US rate reduction next month as the world's biggest economy shows signs of stuttering.
"Anything less than a clear signal that the Fed is open to cutting rates soon in response to building downside risks to the US economic outlook could leave financial markets disappointed," noted MUFG currency analyst Lee Hardman.
"The US rate market is well priced for at least a (quarter-point) rate cut to be delivered by July."
- Hong Kong returns to buying -
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In Hong Kong, investors returned to buying after three days of losses that saw the Hang Seng drop more than two percent after protests against the law -- which would have allowed extradition to China -- turned violent Wednesday.
Another, peaceful, demonstration Sunday saw around two million people take to the streets, according to organisers.
The plan had also spooked business leaders who feared it would damage the city's reputation as an international business hub.
Traders "will breathe a loud sigh of relief today, as on Wednesday when tear gas and rubber bullets were filling the air, the markets were getting extremely jittery that this ticking time bomb was about to explode", said Stephen Innes, managing partner at Vanguard Markets.
"Fortunately, cooler heads prevailed."
In commodities, oil prices retreated from last week's gains that followed tanker attacks in the Gulf of Oman. Washington has blamed Iran for the attacks but Tehran has called the US charges "baseless".
- Key figures around 1120 GMT -
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London - FTSE 100: DOWN 0.2 percent at 7,334.10 points
Frankfurt - DAX 30: FLAT at 12,096.29
Paris - CAC 40: UP 0.2 percent at 5,376.94
EURO STOXX 50: UP 0.1 percent at 3,381.26
Tokyo - Nikkei 225: UP 0.03 percent at 21,124.00 (close)
Hong Kong - Hang Seng: UP 0.45 percent at 27,240.35 (close)
Shanghai - Composite: UP 0.20 percent at 2,887.62 (close)
New York - Dow: DOWN 0.1 percent to 26,089.61
Euro/dollar: UP at $1.1217 from $1.1208 at 2100 GMT
Pound/dollar: DOWN at $1.2517 from $1.2589
Dollar/yen: UP at 108.71 yen from 108.56 yen
Oil - Brent North Sea: DOWN 69 cents at $61.32 per barrel
Oil - West Texas Intermediate: DOWN 63 cents at $51.88