The North Atlantic sea level pressure anomalies (SLPA) associated with El Niqo Southern Oscillation (ENSO) have been analyzed in a quasi-millennial (1000--1990) simulation with the ECHO-G model. In November--December, the ENSO-related SLPA over the North Atlantic area are weak, while a realistic pattern already appears over the North Pacific and North America. In January--March, the SLPA over North Atlantic are stronger and realistic from the North Pacific to Europe: the Aleutian low is strengthened (weakened), SLPA are positive (negative) over the north-central and north-eastern parts of North America, and SLPA display a negative (positive) NAO-like pattern over North-Atlantic during warm (cold) ENSO events, as in observations. The results also confirm the existence of a strong inter-event SLPA associated with warm and cold ENSO events, especially over the North Atlantic, while the relationship is stationary at multidecadal timescales. It seems that neither the intensity nor geographical longitude of the equatorial Pacific sea surface temperature anomaly (SSTA) and intensity of tropical Atlantic SSTA, nor the volcanic forcing, simply introduced here as a decrease of the solar constant, significantly induce an inter-event variability, which seems, in this run, mostly of atmospheric origin.