We study one of multidimensional inverse scattering problems for quantum systems in time-dependent electric fields $E(t)$, whose leading part is represented as $E_0(1+|t|)^{-\mu}$ with $0\le\mu<1$, by utilization of the Enss-Weder time-dependent method. In our previous work, we have dealt with the case where $E(t)$ is a constant electric field. The present work is a continuation of that. The main purpose of this paper is to improve the known results by some methods developed in our previous work. Our methods give an appropriate class of short-range potentials which can be determined by the scattering operators, that seems natural in terms of direct scattering problems.