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This study establishes a linkage between the North Atlantic sea ice concentration (SIC) or sea surface temperature (SST) and cold anomalies over northern Europe and North America through the Greenland blocking (GB) change. It is revealed that the magnitude of the meridional potential vorticity (PV) gradient in the North Atlantic mid- to high latitudes plays a key role in whether strong cold anomalies occur over the North America (NA) or northern Europe (NE) or both, while it is related to the SIC change observed over Baffin Bay, Davis Strait, and the Labrador Sea (BDL collectively) and the North Atlantic SST anomaly. When the midlatitude Atlantic SST is strongly warm or when the BDL SIC anomaly is largely positive, there is a corresponding large PV gradient over the North Atlantic. In this case, no intense cold anomalies are seen over NA due to less westward movement and the short lifetime of GB. Instead, a relatively strong cold anomaly appears over western and southern Europe. Its prior large-scale atmospheric circulation is the positive phase of the North Atlantic Oscillation (NAO). Moreover, strong cold anomalies can simultaneously occur over NA and NE only when the PV gradient is small under the influence of large SIC decline or intense mid- to high-latitude SST cooling across the Gulf Stream Extension. Its prior large-scale atmospheric circulation is a negative NAO phase. Daily composites show that strong cold anomalies over NA occur along the northwest-southeast direction in the presence of large SIC decline, whereas strong cold anomalies occur in NA midlatitudes even in the absence of large BDL SIC decline when mid- to high-latitude SST cooling is strong.