Eurozone services PMI slipped to 52.2 (flash 52.4) in March from 52.6 in February.
Composite output edged down to 53.1 (flash 53.2) from 53.3.
The surveys indicate that the eurozone's recovery is broad, say Markit. Irish PMI hit a seven-year high of 59 and France a 31-month peak of 51.8, but German growth softened.
Still, the eurozone enjoyed the best quarter for PMI in three years in Q1, with the surveys indicating GDP growth of 0.5%.
Weakening price indices are a concern amid fears about deflation, although the survey also shows that companies have become leaner, more productive and therefore more competitive.
The euro is flat at $1.3765. (PR)