Analysts said the report was positive overall but it was still unclear when the European Central Bank might end its massive stimulus programme after years of pumping cheap money into the economy.
Data monitoring company IHS Markit said its April Composite Purchasing Managers Index came in at 56.7 points, the highest reading since April 2011 and up from 56.4 points in March.
The PMI measures companies' willingness to invest in their business and so gives a good idea of how well the underlying economy is performing.
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Any reading above the boom-bust 50 points line indicates the economy is expanding.
IHS Markit said the 19-nation eurozone economy was doing well on all fronts.
"Job creation... rose to the highest for almost a decade as firms boosted operating capacity in line with buoyant demand and widespread optimism about future prospects," it said in a statement.
"Price pressures, meanwhile, remained among the strongest seen over the past six years," it added.
Inflation, which has bumped along for years well short of the ECB's near two-percent target, has picked up recently, reflecting an increase in underlying demand.
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Broken down, the figures showed the services sector -- which accounts for the bulk of economic activity -- rose to 56.2 points in April from 56 points in March.
The manufacturing output PMI meanwhile jumped to 58 points from 57.5.
Political, election uncertainty
Howard Archer at IHS Markit said the report showed the eurozone doing well but cautioned that rising inflation could crimp consumer demand if current limited wage growth does not compensate.
"There is also still considerable scope for political uncertainties to negatively affect growth over the coming months -– with the looming French election currently a key focus of attention," Archer said in a note.
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He said he did not expect the ECB to signal any change in monetary policy until after the German elections in September.
IHS Markit chief business economist Chris Williamson said the report suggested the eurozone would grow by 0.7 percent in the second quarter, compared with 0.6 percent in the first three months of the year.
"Such strong growth, if sustained, will inevitably lead to upward revisions to economists' 2017 forecasts," Williamson said in the statement.
He said exports were getting an additional boost from a weak euro, caused in part by Brexit jitters, while job creation was a major positive.
"Employment growth has accelerated to the best seen for nearly a decade," he noted.
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On the downside, "France's elections pose the highest near-term risk to the outlook but in the lead-up to the vote the business mood has clearly been buoyant," he noted.
France and top EU economy Germany "are enjoying their best growth spells for six years, while elsewhere in the region the pace of expansion has accelerated to a near 10-year high," Williamson added.
