In sombre dress -- the queen in white, the king with a blue tie -- the new monarchs spent an hour with representatives of around 20 victims' groups in the Zurbano Palace in Madrid.
Accompanied by Interior Minister Jorge Fernandez Diaz, they observed a minute's silence to the memory of those killed in attacks by the Basque separatist ETA and left-wing GRAPO, as well as the Madrid train bombings by Islamist radicals in 2004.
The groups welcomed the statement by Felipe during his address to parliament in which he paid homage to the "victims of terrorist violence who lost their lives or who suffered to defend our freedom."
The armed Basque separatist group ETA, which has been weakened by a string of arrests and dwindling popular support for its violent tactics, announced an end to violence in 2011.
Earlier this year the group, which is blamed for the deaths of 829 people in a four-decade campaign for an independent Basque homeland in northern Spain and southwestern France, said it would put its arsenal of weapons "out of operational use".
But it has so far refused to disband or disarm as demanded by the Spanish and French governments.