Momentum and doping dependence of the static charge susceptibility χ (q) in the t- t′ -J model is investigated. Correlations lead to a strongly momentum-dependent renormalization of χ (q). The charge susceptibility near the (π,π) region of the Brillouin zone is strongly suppressed as the hole density δ is decreased. However, contrary to naive expectations, χ (q) around q= (π,0) and (0,π) remains large and practically unchanged at δ∼0.1-0.5. This effect is consistent with a tendency towards low-energy charge fluctuations with the wave vectors along the Γ-X direction, reported in earlier studies. Our main finding is that the above trends are amplified by J -driven pairing effects, indicating that the pseudogap formation may promote the charge inhomogeneity. The next-nearest hopping t′ leads to weakening of the above momentum-selective renormalizations of χ (q). We analyze the effects of long-range Coulomb interaction, taking into account a layered structure of cuprates. As an application, the results are discussed in the context of bond-stretching phonon softening in hole-doped cuprates. In particular, a peculiar doping and momentum dependence of the electron-phonon coupling constant is found.