The archaeointensity records from Greece present several gaps in the prehistoric period among which the ones in the third and second millennia BCE (Early and Middle Bronze Age) are not justified by the abundance of relevant settlements in the broader Greek area. Their excavations yielded numerous collections of pottery and ceramics, well-studied to a big extent from archaeological and archaeometric point of view. We collected six groups of fragments dated from 2200 BCE to 1500 BCE which were subjected to a classical archaeomagnetic study. The material response to the experiments was mostly satisfactory, and the archaeointensity was calculated both with Thellier-Thellier and multispecimen protocols. These results, complemented by the ones recently published for the period 1500-900 BCE, and plotted versus the existing secular variation curves for Greece and relevant geomagnetic field models allow the recovery of a smooth V-shape already suggested for 2 the Middle East. Nevertheless, we only observed a slight intensity maximum around 1900-1800 BCE while the minimum suggested for the Near East around 1800 BCE is probably shifted to an earlier period.