No.
If all it took was gangs of citizens attacking each other, Los Angeles would be in a "civil war." A few hundred die each year in such violence.
It isn't a civil war when the leaders of the factions are negotiating in an organized government, trying to work out a peaceful solution, rather than holed up in bunkers leading their people in battle.
What we have now are thugs and terrorists running around in the streets in Iraq. Note that all of the Iraqi Army is on one side in this "civil war."