Newton never said that, and there's really no such thing as the "force of an object".
Newton said that the rate of change of an object's momentum is equal to the net force ACTING ON the object. These days, almost everybody says that the object's acceleration, multiplied by its mass, is equal to the net force ACTING ON it. This statement is entirely equivalent to the other one.
Newton's 2nd law applies everywhere, to simply all objects.