A sufficient condition for the residual p-finiteness (approximability by the class \(\mathcal{F}_p\) of finite p-groups) of a free product G = (A * B; H) of groups A and B with a normal amalgamated subgroup H is obtained. This condition is used to prove that if A and B are extensions of residually \(\mathcal{N}\)-groups by \(\mathcal{F}_p\)-groups, where \(\mathcal{N}\) stands for the class of finitely generated torsion-free nilpotent groups, and if H is a normal p′-isolated polycyclic subgroup, then the group G is residually p-finite (i.e., residually \(\mathcal{F}_p\)-group), provided the quotient group G/HpH′ is residually p-finite.