Аннотация:We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain thegravitational form factors of the pion in a common approach to its electroweak and gravitational properties.In the preceding work [Phys. Rev. D 103, 014029 (2021)], we formulated the mathematical background,presented the principal scheme of calculation and testified the obtained qualitative results to satisfy thegeneral constraints given by the principles of the theory of hadron structure. In the present work, we givethe detailed calculation of the gravitational form factors in the large range of momentum transfer, their staticlimits, and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we takeinto account the gravitational structure of the constituent quarks. We show that the results are almostinsensitive to the type of model two-quark wave function in a close analogy to the case of the pionelectromagnetic form factor. We present a correct calculation of the form factor D and correspondingmatrix element of the energy-momentum tensor, going beyond the scope of the modified impulseapproximation. Most of the parameters that we use for the calculation had been fixed even earlier in ourworks on the pion electromagnetic form factors. The only free parameter is the D-term of the constituentquark, which we fix by fitting the result for the slope at zero of the normalized to pion D-term form factor Dof the pion, to a chosen experimental value.DOI: 10.1103/PhysRevD.106.054013