With numbers below 50 indicating a contraction, the Markit Eurozone Composite Output Index fell from 46.7 in April to 46 in May in the 17-member eurozone .
The market research firm cited "widespread weakness across the currency union, with output falling across the big-four nations."
The index for Germany came to 49.3, a 34-month low. For France, the index dropped to 44.6, a 37-month low.
Italy's services business index posted a two-month low at 43.5, while Spain's index fell to a 6-month low at 41.2.
"Companies report business activity to have been hit by heightened political and economic uncertainty, which has exacerbated already weak demand both in the euro area and further afield," said Markit Chief Economist Chris Williamson.
"Based on these numbers, it would not be surprising to see (the) gross domestic product for the region contract by 0.5 percent int he second quarter, though an even steeper decline could be seen if the June data disappoint," he said in a statement.
Companies in Europe were "blighted by the persistent weakness of demand, leading to further job losses," the report said. New business orders are near a three-year low for the region.
Markit's Eurozone Service Business Activity Index, also released Tuesday, dropped from 46.9 in April to 46.7 in May, the firm said. The service index, released a weak after the manufacturing index, has shown contraction in eight of the past nine months with Germany the only eurozone country reporting service industry growth in May.