The association between short-term variability in the North Atlantic Oscillation (NAO) and intense geomagnetic storms is analyzed taking into account the solar activity level. The NAO is the dominant pattern of variation in atmospheric circulation in the North Atlantic basin. This oscillation results in a large-scale modulation of the normal patterns of heat and moisture transport, especially in winter, which determines changes in temperature and precipitation in a great area from eastern North America to Central Europe. A positive correlation between long-term variations in the NAO and geomagnetic activity has already been shown in several studies. However, at daily timescales, from the study of more than 200 geomagnetic storms we observe a decrease in the NAO index coincident with the maximum intensity of the geomagnetic storm. An explanation of our result could be given through the upper atmosphere processes induced by geomagnetic storms followed by coupling mechanisms among the different atmosphere regions, reaching finally the troposphere, in the context of an overall increasing trend which may be due to anthropogenic activity. A possible process would be that the NAO decrease due to geomagnetic storms is highly localized in time at daily scales and the high positive correlation between geomagnetic activity indices and NAO, specially after 1970, is due merely to a coincidence of increasing trends in both parameters.