By using the Hamiltonian form of the Maxwell equations, a biquaternionic model of electro-gravimagnetic (EGM) field is proposed. The EGM-field equations, generating different charges and currents, are constructed. The field analogs of three Newton’s laws are formulated for free and interacting charges and currents, as well as the total field of interaction. The Lorentz invariance of the EGM-field equations is investigated (in particular, the charge-current conservation law). It is shown that at the presence of field interaction, this law differs from the well-known one. A new modification of the Maxwell equations is proposed with the scalar resistance field in the biquaternion EGM-field tension. Relativistic transformations of mass and charge-current densities, forces, and their powers are constructed. The solution of the Cauchy problem is given for equation of charge-current transformations.