One- and two-photon ionization of atomic hydrogen by an ultrashort hyperbolic secant laser pulse is analyzed in detail by means of the essential-states method. We consider two frequency regimes. For photon energies close to the ionization potential, we show that the excitation of atomic hydrogen, initially in its ground state, leads, at low and moderate laser intensities, to an np-state population distribution that, for ultrashort pulses, is strongly shifted down to low-lying Rydberg states. At very high intensities in this frequency regime, we show that the time evolution of the Rydberg-state population follows adiabatically the pulse shape and does not lead to population trapping in the Rydberg states. This contrasts with the results obtained in the low-frequency regime. We demonstrate that, when hydrogen is excited from the 2s state, a substantial inhibition of ionization occurs at high field intensities. The stabilization is caused by the creation of a spatially extended wave packet that results from the Raman mixing of intermediate Rydberg states.