  Given a holomorphic submersion of reduced complex spaces, we prove that the
basic Oka property of the submersion implies the parametric Oka property. This
generalizes the corresponding result for complex manifolds (F. Forstneric, Oka
Manifolds, C. R. Acad. Sci. Paris, Ser. I, 347 (2009) 1017-1020). It follows
that a stratified elliptic (or subelliptic) holomorphic submersion, or a
stratified holomorphic fiber bundle whose fibers are Oka manifolds, enjoys the
parametric Oka property. As an application we give a parametric version of the
factorization theorem due to Ivarsson and Kutzschebauch (A solution of Gromov's
Vaserstein problem, C. R. Acad. Sci. Paris, Ser. I 346 (2008) 1239-1243) for
holomorphic maps from finite dimensional reduced Stein spaces to the special
linear group SL_n(C).
