The emission of warm dust dominates the mid-infrared spectra of active galactic nuclei (AGN). Only interferometric observations provide the necessary angular resolution to resolve the nuclear dust and to study its distribution and properties. The investigation of dust in AGN cores is hence one of the main science goals for the MID-infrared Interferometric instrument MIDI at the VLTI. As the first step, the feasibility of AGN observations was verified and the most promising sources for detailed studies were identified. This was carried out in a snapshot survey with MIDI using Guaranteed Time Observations. In the survey, observations were attempted for 13 of the brightest AGN in the mid-infrared which are visible from Paranal. The results of the three brightest, best studied sources have been published in separate papers. Here we present the interferometric observations for the remaining 10, fainter AGN. For 8 of these, interferometric measurements could be carried out. Size estimates or limits on the spatial extent of the AGN-heated dust were derived from the interferometric data of 7 AGN. These indicate that the dust distributions are compact, with sizes on the order of a few parsec. The derived sizes roughly scale with the square root of the luminosity in the mid-infrared, s ~ sqrt(L), with no clear distinction between type 1 and type 2 objects. This is in agreement with a model of nearly optically thick dust structures heated to T ~ 300 K. For three sources, the 10 micron feature due to silicates is tentatively detected either in emission or in absorption. Based on the results for all AGN studied with MIDI so far, we conclude that in the mid-infrared the differences between individual galactic nuclei are greater than the generic differences between type 1 and type 2 objects.