Aims. In this paper we present a classification of emission-line galaxies at intermediate and high redshifts (0.5 z 1.0 for optical spectra, z 2.5 for near-infrared spectra), using the D n (4000) index as a supplementary diagnostic. Our goal is to complement the diagnostic based only on emission-line ratios from the blue part of the spectra, which suffer from some limitations for the classification of Seyfert 2 and composite galaxies. Methods. We used a sample of 89 379 galaxies with a good signal-to-noise ratio from the Sloan Digital Sky Survey (data release 7). Using the classification scheme presented in Paper I, we classified these galaxies with a diagnostic diagram involving the [Oiii]λ5007/Hβ and [Oii]λλ3726 + 3729/Hβ emission-line ratios. Then we derived a supplementary diagnostic involving D n (4000) to improve this classification, in the regions where objects of different types are mixed. To show the validity of our spectral classification we established success-rate and contamination charts, then we compared our results to those obtained with the reference classification scheme that was obtained also using Hα, [Nii]λ6584, and [Sii]λλ6717+6731 emission lines. Results. We show that our supplementary classification based on the D n (4000) index allows to separate unambiguously star-forming galaxies from Seyfert 2 in the region where they were mixed in Paper I. It also significantly reduces the region where star-forming galaxies are mixed with composites.