An archeointensity study was carried out on 14 sites of Syrian baked clay artifacts, archeologically dated between ∼2500 BC and ∼1600 BC. Using an experimental protocol involving high‐temperature magnetization measurements, well‐defined mean intensity values were derived for 13 different sites with three to nine results obtained at the fragment level per site. Results of similar ages are coherent and the new data set is in good agreement with previous archeointensity results obtained from the same region. All together these data allow one to refine the evolution of the geomagnetic field intensity in the Middle East during the third and the second millennium BC. In particular, they show the occurrence of three periods of rather sharp intensity increase at ∼2600 BC, ∼2200 BC and ∼1600 BC possibly at the times of climatic cooling in the eastern North Atlantic, further suggesting a connection between the Earth's magnetic field and multi‐decadal climatic events.