The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a rigorous relativistic model of light ray propagation developed in the framework of General Relativity. The data-processing of the space interferometric observations must rely upon the theory of general-relativistic transformations between the spacecraft, geocentric, and solar barycentric reference systems allowing unique and unambiguous interpretation of the stellar aberration and parallax effects. On the other hand, the algorithm must also include physically adequate treatment of the relativistic effect of light deflection caused by the spherically-symmetric (monopole-dependent) part of the gravitational field of the Sun and planets as well as the quadrupole- and spin-dependent counterparts of it. In some particular cases the gravitomagnetic field induced by the translational motion of the Sun and planets should be also taken into account for unambigious prediction of the light-ray deflection angle. In the present paper we describe the corresponding software program to take into account all classical (proper motion, parallax, etc.) and relativistic (aberration, deflection of light) effects up to the microarcsecond threshold and demonstrate, using numerical simulations, how observations of stars and/or quasars conducted on board a space optical interferometer orbiting the Earth can be processed and disentangled. For numerical simulations the spacecraft orbital parameters and the telescope optical-system-characteristics have been taken to be similar to those in the Hipparcos mission. The performed numerical data analysis verifies that the relativistic algorithm chosen for data processing is convergent and can be used in practice to determine astronomical coordinates and proper motions of stars (quasars) with the required microarcsecond precision. Results shown in the paper have been obtained with a rather small number of stars (a few thousand). Simulations based on a much larger number of stars, e.g., from the Guide Star Catalogue used to model original observations will give more complete information about potential abilities of the space astrometric missions.