Zonally averaged characteristics of the North Atlantic (NA) thermohaline circulation are investigated in different phases of the Atlantic Multidecadal Oscillation (AMO) index over the past 70 years using ocean objective analyses EN4 and WOA13 and reanalyses GFDL, ESTOC, ORA-S4, and GECCO2. It is shown that similar thermohaline patterns appear in zonally averaged climatic trends and in differences in the composites of anomalies of the potential temperature and salinity fields for all data sets. To find out how the variability in the thermohaline state of waters in the NA is accompanied by the variability in its thermohaline circulation, we have analyzed the variability of the Atlantic Meridional Overturning Circulation (AMOC) stream function. The average AMOC stream functions calculated from ocean objective analyses and reanalyses, reflecting the NA thermohaline circulation, are generally similar to each other. Nonetheless, they can be divided according to their spatial structure into two groups: (EN4, WOA13, and GFDL) and (ESTOC, ORAS4, and GECCO2). In their trends and anomaly composite differences, the AMOC stream functions differ significantly among themselves, as well as from EN4 and WOA13. Moreover, the main distinction is in the sign of climatic trends and composite differences, which determines changes in the direction of the zonally averaged thermohaline circulation. It is found that positive and negative temperature (salinity) anomalies in alternating successive phases of the AMO index circulate with a period of roughly 60 years along the pathway of water in the AMOC, sinking into deep ocean layers at about 60 degrees N and rising toward the surface at 25 degrees N. This process is most pronounced for the EN4 and WOA13 objective analyses and ORAS4 reanalysis. It can be assumed that this mechanism contributes substantially to the formation of the AMO index phases.