Context. Several rotational transitions of ortho- and para-water have been identified toward evolved stars in the ground vibrational state as well as in the first excited state of the bending mode (v2 = 1 in (0, 1, 0) state). In the latter vibrational state of water, the 658 GHz J = 11,0−10,1 rotational transition is often strong and seems to be widespread in late-type stars. Aims. Our main goals are to better characterize the nature of the 658 GHz emission, compare the velocity extent of the 658 GHz emission with SiO maser emission to help locate the water layers and, more generally, investigate the physical conditions prevailing in the excited water layers of evolved stars. Another goal is to identify new 658 GHz emission sources and contribute in showing that this emission is widespread in evolved stars. Methods. We have used the J = 11,0−10,1 rotational transition of water in the (0, 1, 0) vibrational state nearly 2400 K above the ground-state to trace some of the physical conditions of evolved stars. Eleven evolved stars were extracted from our mini-catalog of existing and potential 658 GHz sources for observations with the Atacama Pathfinder EXperiment (APEX) telescope equipped with the SEPIA Band 9 receiver. The 13CO J = 6−5 line at 661 GHz was placed in the same receiver sideband for simultaneous observation with the 658 GHz line of water. We have compared the ratio of these two lines to the same ratio derived from HIFI earlier observations to check for potential time variability in the 658 GHz line. We have compared the 658 GHz line properties with our H2O radiative transfer models in stars and we have compared the velocity ranges of the 658 GHz and SiO J = 2−1, v = 1 maser lines. Results. Eleven stars have been extracted from our catalog of known or potential 658 GHz evolved stars. All of them show 658 GHz emission with a peak flux density in the range ≈50–70 Jy (RU Hya and RT Eri) to ≈2000–3000 Jy (VY CMa and W Hya). Five Asymptotic Giant Branch (AGB) stars and one supergiant (AH Sco) are new detections. Three AGBs and one supergiant (VY CMa) exhibit relatively weak 13CO J = 6−5 line emission while o Ceti shows stronger 13CO emission. We have shown that the 658 GHz line is masing and we found that the 658 GHz velocity extent tends to be correlated with that of the SiO maser suggesting that both emission lines are excited in circumstellar layers close to the central star. Broad and stable line profiles are observed at 658 GHz. This could indicate maser saturation although we have tentatively provided first information on time variability at 658 GHz.< Réduire