The private research firm said the headline Purchasing Managers Index for retail reached 49.1 in the month of June.
With numbers below 50 indicating a contraction, that is still below the break-even line. But it is the slowest pace of decline since March 2012, Markit said.
June is also the third consecutive month in which the pace of decline has slowed.
Across the eurozone, the PMI for retail is at a 15-month high. In Germany, the region's largest economy, it is at 55.3, a 16-month high.
In France and Italy, which have the second and third largest economies in the region, the PMI for retail is at 48.9 and 40.7, respectively, which is a 12-month high for France and a 2-month low for Italy. Markit said.
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