Germany and France are outpacing the 17-nation bloc, but periphery nations like the Irish Republic and Greece are struggling, said research group Markit.
Its closely-watched purchasing managers index was 57.8 in April, up from 57.6 in March.
But economists said April's data was flattered by France and Germany.
Any score above 50 indicates economic expansion.
'Faltering demand' The overall figure was the second best since June 2007, and was helped by strong service sector growth in France and good manufacturing expansion in Germany.