Context. Accurate positional measurements of planets and satellites are used to improve our knowledge of their dynamics and to infer the accuracy of planet and satellite ephemerides. Aims: In the framework of the FP7 ESPaCE project, we provide the positions of Mars, Phobos, and Deimos taken with the U.S. Naval Observatory 26-inch refractor during the 1971 opposition of the planet. Methods: These plates were measured with the digitizer of the Royal Observatory of Belgium and reduced through an optimal process that includes image, instrumental, and spherical corrections to provide the most accurate data. Results: We compared the observed positions of the planet Mars and its satellites with the theoretical positions from INPOP10 and DE430 planetary ephemerides, and from NOE and MAR097 satellite ephemerides. The rms residuals in RA and Dec of one position is less than 60 mas, or about 20 km at Mars. This accuracy is comparable to the most recent CCD observations. Moreover, it shows that astrometric data derived from photographic plates can compete with those of old spacecraft (Mariner 9, Viking 1 and 2).