  We give one parameter deformation of level $k$ free field realization of the
screening current of the elliptic algebra $U_{q,p}(sl_2^)$. By means of these
free field realizations, we construct infinitly many commutative operators,
which we call the nonlocal integrals of motion associated with level $k$
realization of the elliptic algebra $U_{q,p}(sl_2^)$. They are given as
integrals involving a product of the screening current and elliptic theta
functions. This paper give level $k$ generalization of the nonlocal integrals
of motion given in [arXiv:0705.0427].
