The Markit Eurozone Purchasing Managers' Index for the eurozone dropped from 48.6 in January to 47.3 in February, Markit's flash estimate indicates.
The break-even point in the index is 50, meaning falling further below 50 indicates a more severe slowdown.
The figures could be revised but the flash estimate for service-oriented firms slipped in February from January's 48.6 to 47.3, while the flash PMI for manufacturing firms dropped from 47.9 to 47.8.
Markit noted that business output rose in Germany, the largest economy in the eurozone, for the third consecutive month, although the gain was at a slower rate than previously. In contrast, Markit said, rates of decline accelerated in France, the second largest economy, and in the rest of the 17-member currency region as a whole.
"A steepening rate of decline in February is a disappointment and suggests that the eurozone is on course to contract for a fourth consecutive quarter in the first three months of the year," said Markit Chief Economist Chris Williamson.
"However, despite the fall in the PMI, the first quarter decline in the economy should be less severe than the 0.6 percent drop in GDP seen in the final quarter of 2012, with a contraction of 0.2-0.3 percent looking likely," he said.