Spatiotemporal evolution of intense circularly polarized Gaussian laser pulse propagating in plasma is investigated. Self-focusing and self-compression properties of the laser pulse are studied, taking into account the ponderomotive nonlinearity, magnetic field, and state of wave polarization effects. The coupled differential equations governing the beam width (in space) and pulse length (in time) parameters are obtained via paraxial ray and Wentze−Kramers−Brillouin approximations and solved numerically. Numerical simulation showed that the pulse is compressed (in time and space) to a significant extent at a different normalized distance due to the effect of the nonlinearity of the medium. It is shown that for the right-hand circularly polarized laser, the strength of both self-focusing and self-compression of the laser pulse along the propagation direction is increased by increasing the value of the magnetic field, and consequently, the normalized intensity of the pulse is enhanced as it propagates through the plasma. In the case of a left-hand circularly polarized laser, an increase in the magnetic field causes a decrease in the strength of both self-focusing and self-compression of the laser pulse, especially in the higher values. To analyse the evolution of the laser spot size, a three-dimensional view of the normalized laser intensity at different points of the distance of propagation has also been plotted. Moreover, the results indicate a specific laser intensity range with a "saturation point" where the compression process reaches its maximum value, and outside of this range, it vanishes.