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In the 17 eurozone countries, construction output was down 2.8% in June, compared with the corresponding month in 2011.
Production in Portugal showed the sharpest fall, down by 18.9% year-on-year in June, while a poor performance by the UK resulted in a 15.5% year-on-year fall.
Hungary and Slovakia both saw construction output fall by 11% year-on-year.
The biggest gains were made in Sweden, where production was up by 4.6%, and in Germany, at 3% year-on-year.
Split along building construction and civil engineering lines, the index showed a fall of 3.2% year-on-year in building construction in the eurozone and a decrease of 5.6% in the 27 member states of the European Union.
Data for civil engineering showed falls of 3.8% in the eurozone and 9.3% in the full EU.