Euro zone manufacturing activity indexes for March, due later, are expected to add to concerns about the fragile global economic recovery revealed in weaker than expected data from China and the United States on Monday.
Policy meetings of the European Central Bank and Bank of Japan on Thursday, along with US jobs data on Friday are also keeping markets on hold.
"Investors are not making big bets following subdued manufacturing data in the United States and China and ahead of two major events later this week," Lee Jae-man, an analyst at Tong Yang Securities in Seoul.
Europe's index of top shares, the FTSEurofirst 300, opened 0.2% higher with Paris's CAC-40, Frankfurt's DAX and London's FTSE 100 around 0.3% up.
MSCI's world equity index was little changed at 358.4 points after losing 0.46% in March for its worst monthly performance since October last year.
The dollar was down 0.15% against a basket of currencies after data on Monday showed slowing US factory activity in March, pointing to an economy losing momentum as government spending cuts bite.
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The euro edged up 0.1% against the generally softer dollar to trade around $1.2870, pulling away from a four-month trough of $1.2750 hit last week as concerns intensified over the consequences of Cyprus's bailout conditions.
The euro's moves were expected to be limited before Thursday's ECB meeting when President Mario Draghi is likely to be quizzed about the deal's implications for the whole region.
Temporary capital controls are in place for Cyprus after the IMF, the European Commission and the ECB imposed a levy on big depositors at the island's two largest banks as part of the financial rescue plan.
"The way the European Union managed the Cypriot crisis has been a disaster, and confidence might take time to come back, so investors will remain cautious for a while," said David Thebault, head of quantitative sales trading, at Global Equities.
Oil and copper, both sensitive to industrial demand, fell as investors focused on Monday's official Chinese factory activity report which was below forecasts.
US crude futures were down 0.2% to $96.88 a barrel although Brent was little changed at around $111 a barrel.
London copper fell 0.9% to $7,469 a tonne, after touching a seven-month low earlier.