Aims. We have investigated a frequency-dependent shift in the absolute position of the optically thick apparent origin of parsec-scale jets ("core shift" effect) to probe physical conditions in ultra-compact relativistic outflows in active galactic nuclei. , and 88 μas, respectively, compared to the typical measured errors of 50, 51, 35 μas. The effect occurs predominantly along the jet direction, with departures smaller than 45 • from the median jet position angle in over 80% of the cases. Despite the moderate ratio of the observed frequencies (<2), core shifts significantly different from zero (>2σ) are detected for about 55% of the sources. These shifts are even better aligned with the jet direction, deviating from the latter by less than 30 • in over 90% of the cases. There is an indication that the core shift decreases with increasing redshift. Magnetic fields in the jet at a distance of 1 parsec from the central black hole, calculated from the obtained core shifts, are found to be systematically stronger in quasars (median B 1 ≈ 0.9 G) than those in BL Lacs (median B 1 ≈ 0.4 G). We also constrained the absolute distance of the core from the apex of the jet at 15 GHz as well as the magnetic field strength in the 15 GHz core region.