Future space-borne astrometry missions, such as Gaia, will be able to determine the optical positions of hundreds of quasars with submilliarcsecond accuracies comparable to those achieved in radio by very long baseline interferometry (VLBI). Comparisons of coordinate systems from space-borne missions and VLBI will be very important, first for investigations of possible systematic errors and second for investigations of possible shifts between centroids of radio and optical emissions in active galactic nuclei. In order to make such a comparison more robust, a program for densification of the grid of radio sources detectable with both VLBI and Gaia was launched in 2006. Program sources are 398 quasars with declinations >-10{deg} that are brighter than 18mag at the V band. The first two observing campaigns were run in 2007-2008. In the third campaign, a set of 291 objects from that list was observed with the VLBA+EVN in 2010-2011 with the primary goal of producing their images with milliarcsecond resolution. In this paper, following the method of absolute astrometry, coordinates of observed sources have been derived with milliarcsecond accuracies from analysis of these observations. The catalog of positions of 295 target sources, estimates of their correlated flux densities at 2.2 and 8.4GHz, and their images are presented. The accuracies of source coordinates are in a range of 2-200mas, with a median of 3.2mas.