An apparatus for inserting rods of a rod bundle from a nuclear reactor fuel assembly into a vessel includes a dense-setting device including: a holding cage for laterally holding the rods together in a given dense packing with mutually parallel longitudinal axes, the cage having a bottom on which one end of each of the rods stand; an insert associated with the holding cage having two ends and guide channels receiving the rods, the guide channels defining an outlet cross section at one end near the bottom with outlet openings disposed according to the given dense packing, and the guide channels defining an inlet cross section at the other end at which the rods are inserted with inlet openings disposed according to the position of the rods in the rod bundle, the insert including a plate having the inlet openings formed therein defining the inlet cross section, the plate being movable toward the outlet cross section against a spring up to a stop; and a pulling tool for pulling the insert out of the holding cage and off the rods in the guide channels, the pulling tool including a hold-down body in the form of a cover washer covering the inlet openings, the cover washer being in a stationary position relative to the holding cage at the inlet cross section for holding the rods disposed in the guide channels.