The influence of Zn and Ni impurities on the normal-state pseudogap of underdoped high-Tc cuprate superconductors is studied using exact diagonalization of effective t - J-like Hamiltonians describing low energy electronic excitations of the CuO2 plane with some of the copper ions replaced with Zn/Ni. The Ni case Hamiltonian has been obtained by a sequence of approximations from a more complete model involving Cu 3d, Ni 3d, and O 2p orbitals. Our main findings are: (i) The width OmegaPG of the pseudogap occurring in the many body density of states, and manifesting itself also in the c-axis infrared conductivity, decreases with increasing Zn concentration as a consequence of a suppression of short range spin correlations. (ii) In the case of one hole and one Ni impurity, the hole is, for realistic values of the model parameters, weakly bound to the Ni site. This causes a slight increase of OmegaPG with respect to the pure case. (iii) Based on this result and further results for 1 to 2 holes and 1 to 2 Ni impurities, we suggest that in the real Ni substituted CuO2 plane OmegaPG is larger than in the pure case due to the binding of the doped holes to the Ni sites and effective underdoping. Our findings clarify the trends observed in the c-axis infrared conductivity data of Zn and Ni substituted (Sm,Nd)Ba2Cu3O7 - delta crystals.