We study the wave-packet dynamics in a two-channel Anderson model with correlated diagonal disorder. To impose correlations in the disorder distribution we construct the on-site energy landscape following both symmetry and antisymmetric rules. The dynamics of an initially localized wave packet is investigated by solving numerically the time-dependent Schrödinger equation. Our numerical data show that symmetric cross correlations have a small impact on the degree of localization of the one-particle eigenstates. In contrast, antisymmetric correlations lead to an effective reduction of the effective degree of disorder, specially in the strong coupling regime, thus resulting in a substantial increase of the wave-packet spread. A finite size scaling analysis shows that the antisymmetric cross correlations, in spite of weakening the localization, do not promote ballistic transport. Theoretical explanations to the effect of cross-correlations in the wave-packet dynamics are provided.