A self-consistent kinetic model based on relativistic Vlasov-Maxwell equations is presented for the generation of quasistatic spontaneous fields, i.e., both the quasistatic magnetic (QSM) field and the quasistatic electric (QSE) field, in intense laser plasma interaction. For the circularly polarized laser, QSM field includes two parts, the axial part B-z as well as the azimuthal B-theta; the QSE field E-s, corresponding to the space-charge potential, forms a plasma density channel. For the linearly polarized laser, B-z is absent. Equations for B-z, B-theta, and E-s are uniformly derived from one self-consistent model under the static-state approximation, which satisfies the conservation law of charge. The profile of the plasma density channel and the dependence of the peak QSM fields on the laser intensity are discussed. The experiment and simulation results are explained by the model. The predicted QSM and QSE fields are also observed in the three-dimensional particle simulation. (c) 2005 American Institute of Physics.