No, there is not.

https://law.justia.com/codes/new-jersey/2016/title-2c/section-2c-3-4/

The only part of the statute that mentions anything akin to a warning is the section that deals with establishing what a "reasonable belief" is. As I just responded to someone else regarding this, I'll just copy pasta:

(2)A reasonable belief exists when the actor, to protect himself or a third person, was in his own dwelling at the time of the offense or was privileged to be thereon and the encounter between the actor and intruder was sudden and unexpected, compelling the actor to act instantly and:

(a)The actor reasonably believed that the intruder would inflict personal injury upon the actor or others in the dwelling; OR

b)The actor demanded that the intruder disarm, surrender or withdraw, and the intruder refused to do so.

The emphasis on OR is mine, because you don't need both conditions to be fulfilled to have a reasonable belief - it's one or the other. If someone breaks into your home, and you tell them to leave, and they refuse, then that provides the reasonable belief that they intend to cause serious injury or death to you or others.