ABSTRACT We have performed a very long baseline interferometry (VLBI) survey of local (z < 0.05) ultrahard X-ray (14–195 keV) selected active galactic nuclei (AGNs) from the Swift Burst Alert Telescope (BAT) using KVN, KaVA, and VLBA. We first executed fringe surveys of 142 BAT-detected AGNs at 15 or 22 GHz. Based on the result from the fringe surveys and archival data, we find 10/279 nearby AGN (∼4 per cent) VLBI have 22 GHz flux above 30 mJy. This implies that the X-ray AGNs with a bright nuclear jet are not common. Among these 10 radio-bright AGNs, we obtained 22 GHz VLBI imaging data of our own for four targets and reprocessed archival data for six targets. We find that, although our 10 AGNs observed with VLBI span a wide range of pc-scale morphological types, they lie on a tight linear relation between accretion luminosity and nuclear jet luminosity. Our result suggests that a powerful nuclear radio jet correlates with the accretion disc luminosity. We also probed the Fundamental Plane of black hole activity at VLBI scales (e.g. few milliarcsecond). The jet luminosity and size distribution among our sample roughly fit into the proposed AGN evolutionary scenario, finding powerful jets after the blow-out phase based on the Eddington ratio (λEdd)–hydrogen column density (NH) relation. In addition, we find some hints of gas inflow or galaxy–galaxy merger in the majority of our sample. This implies that gas supply via tidal interactions in galactic scale may help the central AGN to launch a powerful parsec-scale jet.