<p>It is quite possible that a few Earth mass (or sub-Earth mass) planetary embryos form among the giant planets. We study the origin of distant trans-Neptunian objects under collective gravity of the migrating giant planets, planetary embryos and massive planetesimals. We carry out the full <i>N</i>-body numerical simulations of gravitational interactions of the giant planets and smaller bodies of different mass ranges for 4 Gyr. The dynamical process of the production of distant trans-Neptunian objects with additional planetary embryos is more efficient than in the four-planet Nice model, which includes only the outer planetesimal disk. In the model with planetary embryos, the number of distant trans-Neptunian objects remaining after 4 Gyr is on average larger at the same initial mass of the outer planetesimal disk. In the presence of planetary embryos, the range of possible final configurations is rather broad. Nevertheless, we have found many cases of the planetary systems that have survived for the Solar System age with a configuration close to the present one. In such systems, the presence of distant trans-Neptunian objects is typical. The dynamical features of objects in the remote trans-Neptunian region are very diverse and include mutual secular resonances and close encounters. The combined action of perturbations from the giant planets, planetary embryos and self-gravity of the planetesimal disk can produce distant trans-Neptunian objects in both high-eccenricity and near-circular orbits. In our simulations, massive objects are injected into the planetary region throughout the age of the Solar System, leading to changes of orbital elements of the giant planets.</p>