We present accurate maps of the CO J = 2-1 and 1-0 lines made with the Plateau de Bure interferometer of the gas disk around the central star(s) of the Red Rectangle, a well known protoplanetary nebula. We confirm that the molecular gas in this source forms a disk perpendicular to the conspicuous axis of symmetry of the optical nebula and that this disk is in rotation. We present detailed modeling of the CO emission and extensive discussion of the accuracy of the values fitted for the different. parameters. The outer radius of the disk is similar to 2.7 x 10(16) (D(pc)/710) cm, as a function of the assumed distance D, which is thought to vary between 380 and 710 pc. The rotation is found to be Keplerian, at least in the inner disk. From this velocity field, we derive a central mass between 0.9 M circle dot, for a distance of 380 pc, and 1.7 M circle dot, for 710 pc. Previous studies of the nature of the stellar component favor the highest values. In the outer disk, we deduce the presence of a slow expansion velocity (similar to 0.8 km s(-1)), superimposed on rotation. We find gas temperatures decreasing from similar to 400 to 30 K across the disk and densities greater than or similar to 3 x 10(4) cm(-3).