Proper motions of more than 6000 stars within 1.0 pc of Sagittarius A* are measured with a mean velocity uncertainty of 12 km/s. There is evidence for tangential anisotropy in the innermost arcseconds, probably related to a well-known disk of massive, young stars in this region. The cluster appears isotropic at projected distances 0.4-1.1 pc from Sgr A*. The Keplerian fall-off of the velocity dispersion due to the point mass of Sgr A* is clearly detectable only inside 0.3 pc. At larger distances, the projected velocity dispersion is constant, with a value of 100 km/s. No evidence for an overall rotation of the cluster is found. Isotropic and anisotropic Jeans models require the presence of an extended mass of 0.5-2.0 x 10^6 solar masses in the central parsec, in addition to the black hole. The influence of the extended mass on the gravitational potential becomes notable at distances beyond about 0.3 pc from Sgr A*. This is the first time that the distributed mass around the MW supermassive black hole has been dynamically detected.