The 50-point mark separates expansion from contraction, and although the region's composite reading remains in positive territory, it has now slipped for the second month in a row.
However Chris Williamson, Markit's chief economist, said that, overall, the extent of the slowing should not be a concern, and highlighted the encouraging developments in hiring.
"Job creation is running at the highest rate for four years as employers remain upbeat about the business outlook, especially in manufacturing where the weaker euro appears to be helping drive strong export sales," he said in a note.
"But there are worrying signs of confidence waning in the service sector compared to the wave of optimism seen earlier in the year."
Markit said this month's survey suggested that growth could continue to soften in June. In a statement it said that faster growth in manufacturing was offset by a slowdown in services, "though the pace in the latter merely eased slightly further from March's eight month high to suggest a broad-based upturn remains in place.
Breaking down the PMI figures by country, in France, the composite index rose to a two-month high of 51.0 but in Germany, the index fell to a five-month low of 52.8.
However, job creation gathered momentum in both Germany and France, with the latter enjoying its best spell of hiring in over three years.
For the 19-country euro zone as a whole, the figures point to a slowdown in economic growth in the second quarter, one economist warned, after a pickup in first three months of 2015.
"On past form, the survey is now consistent with quarterly gains in GDP of around 0.3 percent (in the second quarter), a touch smaller than Q1's 0.4 percent," Jonathan Loynes, chief European economist at Capital Economics, said in a note Thursday.
"Overall, (the data are) another warning that the euro-zone economy is set to remain too weak to allow the peripheral countries to grow their way out of their debts."