We consider Ntimes N Hermitian random matrices H consisting of blocks of size Mge N^{6/7}. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H-z)^{-1} satisfy the local semicircle law with spectral parameter z=E+mathbf {i}eta down to the real axis for any eta gg N^{-1}, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for eta gg M^{-1}. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.