We present a remeasurement of old photographic plates, providing important raw data for dynamical studies of the Saturnian satellite system. The unprecedentedly accurate realization of the Gaia reference frame allows us to make a precise calibration of digitized astronegatives of the Saturnian satellite images. We reprocessed 357 astronegatives taken with the 26-inch refractor and the normal astrograph of the Pulkovo Observatory between 1972 and 2007 to obtain the positions of the main Saturnian moons in the second Gaia data release (Gaia DR2) system. Photographic plates were digitized with the Pulkovo Mobile Digitizing Device (MDD) scanner. The New Astrometric Reduction of Old Observations (NAROO) digitizer at the Paris Observatory was used to calibrate the scanned images. Satellite image centering and astrometric reduction were performed. In total, 6487 positions (equatorial coordinates) have been determined with an accuracy of 50mas. This is confirmed by a comparison of our data with modern ephemerides. The verification of the results was performed using data from past close approaches by Saturnian satellites to Gaia reference stars, showing the adequacy of the current residual analysis. A joint review of the Pulkovo and the United States Naval Observatory (USNO) intersatellite positions allows us to conclude about the existence of faint systematic effects in the satellite theories of motions at the 10mas level.