We demonstrate the generation of high magnetic fields for condensed matter research using a high-power laser system. A cavity in which a seed magnetic field is applied is compressed by a kJ ns laser pulse. The time history of the compressed magnetic field is monitored by observing the Faraday effect rotation of polarization of a probe pulse in a glass fiber. To maintain a low-temperature condition in the final high-field region, we put a high-resistance foil around the final compression area. If we assume the length of the compression region is equal to the laser spot size, a magnetic field of more than 800 T is observed by Faraday rotation. Because of the large mass of the compression foil, this high magnetic field is sustained during almost 2 ns. During compression, a rarefaction wave from the backside of the accelerated foil and expanding material from the inner protection foil affect the magnetic field compression history, but the final compressed magnetic field strength agrees with the ratio between the initial sample area and the compressed cavity area.