The iterative configuration interaction (ICI) method is applied to molecular systems within finite basis using only few (1-3) variables and shown to give the exact results that are identical to the full CI (FCI) ones. Since each iteration step of ICI is variational, the ICI converges monotonically to the exact solution from above. The diagonalization in ICI is so slight as the number of variables is so small, in contrast to the huge number of variables of FCI. We calculated the molecular ground states of various spin-space symmetries using minimal basis and double zeta basis. The number of iterations for convergence was small for minimal basis but moderate for double zeta basis, considering that only 1-3 variables are optimized in each iteration step.