The relationship between polar mesosphere summer echoes (PMSE) and geomagnetic disturbances (represented by magnetic K indices) is examined. Calibrated PMSE reflectivities for the period May 2006-February 2012 are used from two 52.0/54.5 MHz radars located in Arctic Sweden (68 degrees N, geomagnetic latitude 65 degrees) and at two different sites in Queen Maud Land, Antarctica (73 degrees/72 degrees S, geomagnetic latitudes 62 degrees/63 degrees). In both the Northern Hemisphere (NH) and the Southern Hemisphere (SH) there is a strong increase in mean PMSE reflectivity between quiet and disturbed geomagnetic conditions. Mean volume reflectivities are slightly lower at the SH locations compared to the NH, but the position of the peak in the lognormal distribution of PMSE reflectivities is close to the same at both NH and SH locations, and varies only slightly with magnetic disturbance level. Differences between the sites, and between geomagnetic disturbance levels, are primarily due to differences in the high-reflectivity tail of the distribution. PMSE occurrence rates are essentially the same at both NH and SH locations during most of the PMSE season when a sufficiently low detection threshold is used so that the peak in the lognormal distribution is included. When the local-time dependence of the PMSE response to geomagnetic disturbance level is considered, the response in the NH is found to be immediate at most local times, but delayed by several hours in the afternoon sector and absent in the early evening. At the SH sites, at lower magnetic latitude, there is a delayed response (by several hours) at almost all local times. At the NH (auroral zone) site, the dependence on magnetic disturbance is highest during evening-to-morning hours. At the SH (sub-auroral) sites the response to magnetic disturbance is weaker but persists throughout the day. While the immediate response to magnetic activity can be qualitatively explained by changes in electron density resulting from energetic particle precipitation, the delayed response can largely be explained by changes in nitric oxide concentrations. Observations of nitric oxide concentration at PMSE heights by the Odin satellite support this hypothesis. Sensitivity to geomagnetic disturbances, including nitric oxide produced during these disturbances, can explain previously reported differences between sites in the auroral zone and those at higher or lower magnetic latitudes. The several-day lifetime of nitric oxide can also explain earlier reported discrepancies between high correlations for average conditions (year-by-year PMSE reflectivities and K indices) and low correlations for minute-to-day timescales.