Ahead of what could be worse figures for April as fallout from the Cyprus situation begins to bite, Markit's Flash eurozone composite Purchasing Managers' Index, seen as a reliable economic growth indicator for the bloc, fell more than expected to 46.5 in March from 47.9 in February.
The figures will fuel concerns that austerity measures imposed by Brussels that force eurozone countries to cut their debts will prolong the recession. In contrast, manufacturing in the US and China improved, which will be important for overall global growth.
"The sharp decline in the flash composite PMI in March pours cold water on hopes of an imminent end to the eurozone recession," said Martin van Vliet, economist at ING.
"If the situation surrounding Cyprus spirals out of control, the onset of recovery might well be delayed."
French businesses had their worst month in four years, likely pushing the eurozone's second-biggest economy into recession. Germany also showed signs of fatigue.
Markit's Flash US Manufacturing Purchasing Managers Index rose to 54.9 this month from 54.3, and the pace of hiring in the sector increased.
A separate Philadelphia Federal Reserve Bank report showed factory activity in the mid-Atlantic region grew in March.
"With manufacturing a reliable bellwether of the rest of the economy, gross domestic product will have risen at a much improved rate" over the first three months of 2013, said Chris Williamson, chief economist at Markit.
The US economy grew at 0.1% in the fourth quarter of 2012, but economists are forecasting first-quarter growth of about 2%.
Another hopeful sign for the US: sales of existing homes hit a three-year high in February and prices rose.
In China, factories increased their output after a holiday dip, suggesting solid, if not spectacular, first-quarter growth in the world's second biggest economy.
The HSBC China PMI for March rose to 51.7 from 50.4, but remained below a two-year high reached at the start of the year.
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