To simply complete the assembly of a fluid dispenser with a follower piston.

A fluid dispenser comprises a lower subassembly constituted of a hollow main body 24 storing a follower piston and an upper subassembly constituted of a pump 14, its push button 16 and a holding element 130. The pump is set on the holding element by snap engaging a flange 196 of a sleeve 190 of the holding element with a housing 144 formed between the flange 140 and a rib 142 of the pump. The hollow main body is filled with a fluid, and then the holding element of the upper subassembly is fitted on the main body by snap engaging its bead 202 with a channel 36 of a neck 32 of the main body, by which the assembly of the dispenser is completed. A protective cover covering the push button is snap engaged with a shoulder 162 of an outer cap 160 of the holding element.