Ring-shaped morphologies of nuclear star-forming regions within the central 40{-}200 pc of disk galaxies have been barely resolved so far in three composite Sy 2 nuclei, the Sy 2 Circinus galaxy and in three non-AGN galaxies. Such morphologies resemble those of the standard 1 kpc-size nuclear rings that lie in the inner Lindblad resonance regions of disk galaxies and, if they have a similar origin, represent recent radial gas inflows tantalisingly close to the central supermassive black holes. We aim to identify the population of such ultra-compact nuclear rings (UCNRs) and study their properties in relation to those of the host galaxies. From archival Hubble Space Telescope UV and Hα images and from dust structure maps of the circumnuclear regions in nearby galaxies, we analyse the morphology of the star formation and dust, specifically searching for ring structures on the smallest observable scales. In a sample of 38 galaxies studied, we have detected a total of four new UCNRs, 30{-}130 pc in radius, in three different galaxies. Including our confirmation of a previous UCNR detection, this yields a UCNR fraction of roughly 10%, although our sample is neither complete nor unbiased. For the first time we resolve UCNRs in two LINERs. Overall the UCNR phenomenon appears widespread and limited neither to late-type galaxies nor exclusively to AGN hosts.