Experiments with interacting high-velocity flows in a laser plasma can help answer fundamental questions in plasma physics and improve understanding of the mechanisms behind some astrophysical phenomena, such as the formation of collisionless shock waves, deceleration of accretion flows, and evolution of solar and stellar flares. This work presents the first direct experimental observations of stagnation and redirection of counterstreaming flows (jets) of laser plasma induced by intense laser pulses with intensity I ∼ $2 \times 10^{18}$ W/cm$^2$. Hybrid particle-in-cell–fluid modeling, which takes into account the kinetic effects of ion motion and the evolution of the pressure tensor for electrons, demonstrates the compression of counterdirected toroidal self-generated magnetic fields embedded in counterstreaming plasma flows. The enhancement of the toroidal magnetic field in the interaction region results in plasma flow stagnation and redirection of the jets across the line of their initial propagation.