Current models of the formation of comets in the Solar System assume that the most likely formation site for these pristine objects is in the Uranus-Neptune zone or just beyond with subsequent dynamical ejection by the growing protoplanets to distant orbits to form the Oort cloud. However, the composition of the recently disintegrated comet C/1999 S4 LINEAR suggests that it was most likely formed in the Jupiter-Saturn region (Mumma et al. 2001b; Kawakita et al. 2001). In this paper we argue that cometesimals could easily appear inside exterior resonances resulting from gas drag, between the orbits of Jupiter and Saturn and beyond Saturn, during the formation of these giant planets. Then, the trapped material could evolve into actual comets by means of collisional coagulation, followed by gravitational instability of a layer of macroscopic bodies or two-body accretion. Properties of these objects would be rather different from those found in classical comets formed beyond Neptune as a result of different physicochemical environment. Our results also suggest that temporarily stable cometary belts may have existed in the Jupiter-Saturn region. We also discuss the implications of this scenario on the existence of a bimodal Centaur population.