Chris Williamson, chief economist at Markit, said: "Even hiring in Germany has almost ground to a halt due to a further drop in new business, suggesting that the brief improvement in business conditions seen at the start of the year is running out of steam.
"French companies meanwhile reported a drop in activity for the first time in four months, and the first cut in staffing levels since last September. Germany and France look to have avoided a return to recession, but only by very narrow margins."
He added: "Elsewhere in the eurozone the situation is worse, with both business activity and employment falling sharply again in March."
Meanwhile the HSBC 'flash' PMI, the earliest indicator of China's industrial activity, fell back to 48.1 in March from 49.6 in February. It was the fourth monthly drop in a row - only this month the contraction was faster.
Filip Petersson, commodity strategist at SEB in Stockholm, told reporters: "We should expect more turbulence as people assess whether China is heading for a hard or a soft landing."