All but three (M87, BL Lac, and 3C 279) extragalactic sources detected so far at very high energy gamma-rays belong to the class of high-frequency-peaked BL Lac objects. This suggested to us a systematic scan of candidate sources with the MAGIC telescope, based on the Donato et al. compilation of X-ray blazars. The observations took place from 2004 December to 2006 March and cover northern sky sources visible under small zenith distances zd 30 degrees at culmination, constraining the declination to -2 degrees to +58 degrees. The sensitivity of the search was planned for detecting X-ray-bright [F(1 keV) > 2 mu Jy] sources emitting at least the same energy flux at 200 GeV as at 1 keV. To avoid strong gamma-ray attenuation close to the ener...