A system for bringing two blood vessels into abutment includes two clamps Pc and a rod 260 connecting the two clamps together by being engaged in two through holes 250 made respectively in the two clamps, a portion of the rod lying between the two clamps possessing two moments of inertia Mi1, Mi2 of different values along two mutually orthogonal directions, one of which is perpendicular to the first plane P1, the smaller value moment of inertia Mi1 being that defined substantially along the direction that is perpendicular to the first plane P1. The system is applicable to bringing two blood vessels into abutment, in particular for the purpose of suturing them.