He was speaking after the ceremonial opening of government offices in this winter capital.
The Durbar move is a more than a century-old practice in Jammu and Kashmir when the seat of government shifts to Jammu in winter and to Srinagar with the onset of summer.
The practice was started by Dogra rulers of the state in the 1870s.
Abdullah had injected a new urgency in the removal of the AFSPA in October last year when he proclaimed that it would be withdrawn from some parts of the state within "the next few days".
He has since faced questions on when that promise would be made good.
The chief minister said Monday: "AFSPA will go. But when, I cannot tell, for no deadline has been set at this stage."
Asked about the threat of the Pakistan-based separatist leader Syed Salahuddin to target village heads in the state, Abdullah said the government would take measures to deal with it.