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We study laser excitation of a hydrogen atom in the presence of a static electric field in the energy region slightly above the zero-field photoionization threshold. With the help of a multiple-scattering expansion, we derive an analytic expression for the time evolution of the initial-state probability, which is nonperturbative with respect to the laser field and which is asymptotically valid in the limit of small electric fields. This allows us to study how the characteristics of the classical periodic orbit, which qualitatively has been associated with the Stark-induced resonances above the zero-field photoionization threshold, manifest themselves in the dynamics of the laser-excitation process.