Detailed studies of the stellar populations of intermediate-redshift galaxies can shed light onto the processes responsible for the growth of the massive galaxy population in the last 8 billion years. We here take a step toward this goal by means of deep, multiobject rest-frame optical spectroscopy, performed with the Inamori Magellan Areal Camera and Spectrograph on the Magellan telescope, of a sample of ~70 galaxies in the Extended Chandra Deep Field South survey with redshift 0.65<=z<=0.75, apparent R>22.7 mag_Vega_, and stellar mass >10^10^ M_{sun}_. We measure velocity dispersion and stellar absorption features for individual sources. We interpret them by means of a large Monte Carlo library of star formation histories, following the Bayesian approach adopted for previous low redshift studies, and derive constraints on the stellar mass, mean stellar age, and stellar metallicity of these galaxies. We characterize for the first time the relations between stellar age and stellar mass and between stellar metallicity and stellar mass at z~0.7 for the galaxy population as a whole and for quiescent and star-forming galaxies separately. These relations of increasing age and metallicity with galaxy mass for the galaxy population as a whole have a similar shape as the z~0.1 analog derived for Sloan Digital Sky Survey galaxies but are shifted by -0.28 dex in age and by -0.13 dex in metallicity, at odds with simple passive evolution. Considering z=0.7 quiescent galaxies alone, we find that no additional star formation and chemical enrichment are required for them to evolve into the present-day quiescent population. However, other observations require the quiescent population to grow from z=0.7 to the present day. This growth could be supplied by the quenching of a fraction of z=0.7 M_{sstarf}_>10^11^ M_{sun}_ star-forming galaxies with metallicities already comparable to those of quiescent galaxies, thus leading to the observed increase of the scatter in age without affecting the metallicity distribution. However, rapid quenching of the entire population of massive star-forming galaxies at z=0.7 would be inconsistent with the age- and metallicity-mass relations for the population as a whole and with the metallicity distribution of star-forming galaxies only, which are, on average, 0.12 dex less metal rich than their local counterparts. This indicates chemical enrichment until the present in at least a fraction of the z=0.7 star-forming galaxies in our sample.