The internal control problem for the Kadomtsev-Petviashvili II equation, better known as KP-II, is the object of study in this paper. The controllability in L-2(T-2) from a vertical strip is proved using the Hilbert uniqueness method through the techniques of semiclassical and microlocal analysis. Additionally, a negative result for the controllability in L-2(T-2) from a horizontal strip is also shown.