Context. Globular clusters are useful for testing the validity of Newtonian dynamics in the low acceleration regime typical of galaxies, without the complications of non-baryonic dark matter. In the absence of disturbing effects, such as tidal heating, the velocity dispersion of globular clusters is expected to vanish at large radii. If this is not observed, and in particular if, as observed in elliptical galaxies, the dispersion is found to be constant at large radii below a certain threshold acceleration, this might indicate a breakdown of Newtonian dynamics. Aims: To minimize the effects of tidal heating that can increase the velocity dispersion at large radii, we study the velocity dispersion profile of two distant globular clusters, NGC 1851 and NGC 1904. Methods: The velocity dispersion profile is derived from accurate radial velocity measurements, obtained at the ESO 8m VLT telescope with the FLAMES multi-object spectrograph. Reliable data for 184 and 146 bona fide cluster star members were obtained for NGC 1851 and NGC 1904, respectively. Results: These data allow us to trace the velocity dispersion profile to ~ 2r0, where r0 is the radius at which the cluster internal acceleration of gravity is a0 ~ 10-8 cm s-2. It is found that in both clusters the velocity dispersion is maximal at the center, decreases moving outward, and then becomes constant beyond ~ r0. Since the distance of these clusters from the Milky Way is large, the observed flattening of the velocity dispersion profile cannot be ascribed to tidal heating effects, as proposed in the case of nearer globular clusters. Conclusions: These results are in full agreement with those found for another five globular clusters previously investigated as part of this project. Taken together, our results for these 7 clusters support the claim that the velocity dispersion is constant beyond r0, irrespectively of the specific physical properties of the clusters: mass, size, dynamical history, and distance from the Milky Way. The strong similarity to the constant velocity dispersion observed in elliptical galaxies beyond r0 is indicative of a common origin for this phenomenon in the two class of objects, and possibly a breakdown of Newtonian dynamics below a0. Based on observations collected at the European Southern Observatory, Chile (Proposal 80.D-0106).Tables 2 and 3 are only available in electronic form at http://www.aanda.org