Hubble Space Telescope images of NGC 3379 show that the V and I luminosity profiles in the inner 13" of this E1 galaxy are represented by two different components: a stellar bulge following a Sérsic law with exponent n=2.36 and a central core (r<0.7") with a characteristic ``cuspy'' profile. Subtraction of the underlying stellar component represented by the fitted Sérsic profile revealed the presence of a small (r~105 pc) dust disk of about 150 Msolar, oriented at P.A.=125deg and inclined ~77 deg with respect to the line of sight. The same absorption structure is detected in the color index (V-I) image. The stellar rotation in the inner 20" is well represented by a parametric planar disk model, inclined ~26 deg relative to the plane of the sky and with apparent major axis along P.A.~67deg. The gas velocity curves in the inner 5" show a steep gradient, indicating that the gas rotates much faster than the stars, although in the same direction. The velocity field of the gaseous system, however, is not consistent with the simple model of Keplerian rotation sustained by the large (7x109 Msolar within a radius of ~90 pc) central mass implied by the maximum velocity observed, but the available data preclude a more detailed analysis. Based on observations obtained at the ESO 3.6 m telescope.