By means of the renormalization-group approach, the scaling behavior of the correlation functions in stochastic magnetohydrodynamics is studied for the case of developed turbulence. To complete the results obtained previously, we investigate the infrared asymptotics of the Green's functions with an arbitrary number of external fields in both the "kinetic" and "magnetic" regimes. Special consideration is given to the problem of dynamic scaling behavior in the magnetic regime. The critical dimensions of the composite operators of the energy functional are calculated. Using the short-distance expansion, we find the relation between the correlation functions within the inertial range and the integral turbulence scale.