Let G be the free product of nilpotent groups A and B of finite rank with amalgamated cyclic subgroup H, H ≠ A and H ≠ B. Suppose that, for some set π of primes, the groups A and B are residually F, where F is the class of all finite p-groups. We prove that G is residually F if and only if H is F-separable in A and B.