The Purchasing Managers Index for Ireland came to 53 in September, Markit said.
With numbers above 50 indicating growth, even Germany's economy, the largest in Europe, showed a continuing slowdown. The PMI in Germany came to 49.2 in September, a four-month high, Markit said.
Ireland's PMI is a 17-month high, Markit said in a report that includes the final estimate of the combined manufacturing and service sector PMI for September for the 17-nation currency region.
Italy's PMI reached a 6-month high at 44.8, while the PMI in France registered 43.2, a 42-month low.
In Spain, which has the fourth-largest economy in Europe, the PMI came to 41.2, a four-month low.
For the region as a whole, the composite PMI and the service sector PMI were in step at 46.1. The previous estimate, called the flash estimate, had the composite PMI for the eurozone at 45.9, while the service sector estimate had been 46.
"It seems inevitable that the region will have fallen back into recession in the third quarter. After falling by 0.2 percent in the second quarter, a steeper fall in output is likely for the third quarter," said Markit Chief Economist Chris Williamson.
"Although there were some signs of stabilization in Germany, any hopes for optimism that the current downturn has bottomed out are tempered by news of steepening rates of contraction in France and Spain, and an ongoing severe downturn in Italy," he said.