P_SPARSLIB is a library of portable FORTRAN routines for parallel sparse matrix computations. The current thrust of the library is in iterative solution techniques. In this paper we present the "accelerators" part of the library, which comprise the best known of the Krylov subspace techniques. The iterative solution module is implemented in reverse communication mode in order to allow any preconditioner to be combined with the package. In addition, this mechanism allows us to ensure portability, since the communication calls required in the iterative solution process are hidden in the dot-product, the matrix-vector product and preconditioning operations.