We study integral convolutions defined on functions ofn variables in symmetric spaces and obtain new additive estimates for the mean value of the nonincreasing permutation(K*f)**(t) of the absolute value of the integral convolution on the interval [0,t] for anyt>0. As an example of application of the estimates obtained, we prove the boundedness of the integral convolution operator acting from the intersection of symmetric spaces into the Marcinkiewicz space.