The local radio-loud AGN population is dominated by compact sources named FR0s. These sources show features, for example the host type, the mass of the supermassive black hole (SMBH), and the multi-band nuclear characteristics, that are similar to those of FRI radio galaxies. However, in the radio band, while FR0 and FRI share the same nuclear properties, the kiloparsec-scale diffuse component dominant in FRI is missing in FR0s. Previous very-long-baseline interferometry (VLBI) observations of a small sample of FR0s show a complex structure, mostly symmetric (two-sided jets) with respect to the central core. With this project we would like to study the parsec-scale structure in FR0s in comparison with that of FRI sources. Jets in FRI are relativistic on the parsec scale and decrease their velocity becoming subrelativistic on the kiloparsec scale. We would like to test whether this result also applies to the jets in FR0s or, alternatively, whether they are subrelativistic on the parsec scale. This might be the reason why they are unable to grow, because of instabilities, related to a low jet bulk velocity. To this end we observed 18 FR0 galaxies with the VLBA at 1.5 and 5GHz and/or with the EVN at 1.7GHz and produced detailed images at milliarcsec resolution of their nuclear emission to study the jet and core structure. All sources have been detected but one. Four sources are unresolved, even in these high-resolution images; jets have been detected in all other sources. We derived the distribution of the jet-to-counter-jet ratio of FR0s and found that it is significantly different from that of FRIs, suggesting different jet bulk speed velocities. Conclusions. Combining the present data with published data of FR0 with VLBI observations, we derive that the radio structure of FR0 galaxies shows strong evidence that parsec-scale jets in FR0 sources are mildly relativistic with a bulk velocity on the order of 0.5c or less. A jet structure with a thin inner relativistic spine surrounded by a low-velocity sheath could be in agreement with the SMBH and jet launch region properties