In this paper, we study the effect that planetary embryos spread between ~0.5 and 4 AU would have on primordial asteroids. The most promising model for the formation of the terrestrial planets assumes the presence of such embryos at the time of formation of Jupiter, or at least of its core. At the end of their runaway growth phase, the embryos are on quasi-circular orbits, with masses comparable to the Moon or Mars. Due to gravitational interaction among them, and with the growing Jupiter, their orbits begin to cross each other, and they collide, forming bigger bodies. As a general outcome, a few planets are formed in a stable configuration in the terrestrial planet region, while the asteroid belt is cleared of embryos. Due to the combined gravitational interaction from Jupiter and from the embryos, the primordial asteroids are dynamically excited. Most of the asteroids are ejected from the system in a very short time, the dynamical lifetime being of the order of 1 My. A few particles survive (less than 1%), mostly in the 2.8-3.3 region, and their eccentricity and inclination distribution qualitatively resembles the observed one. The surviving particles have undergone changes in semi-major axis of several tenth of an AU, which could explain the radial mixing of asteroid taxonomic types. If the distribution of massive embryos is truncated beyond 3 AU, we obtain too many asteroids in the outer part, especially too many Hildas. Thus the forming Jupiter should not have prohibited the formation of large embryos in the outer belt and should no have accreted them too early while still growing. Some of the particles initially in the asteroid belt, as well as some initially in the terrestrial planet region, end up on very inclined eccentric orbits in the inner Solar System, on orbits with a longer decay time. These particles could be the source of the Late Heavy Bombardment.