Introduction Numerous studies have explored the linguistic and executive processes underlying verbal fluency using association designs, which provide limited evidence. To assess the validity of our model, we aimed to refine the cognitive architecture of verbal fluency using an interference design. Methods A total of 487 healthy participants performed letter and semantic fluency tests under the single condition and dual conditions while concurrently performing a secondary task that interferes with speed, semantics, phonology, or flexibility. We examined the effect of such interference on fluency indices including correct responses, clustering, switching, and time course. Results (1) All secondary tasks decreased fluency ( p < 0.0001, all), (2) including a simple concurrent task that solely engages the attentional activation system (i.e., speed interference) and (3) a complex concurrent task that affects the ability to alternate (i.e., flexibility interference). (4) Linguistic secondary tasks (which engage phonological and semantic processes, in addition to attention) led to a greater decrease in fluency than speed interference ( p < 0.0001), (5) with a more pronounced decrease in semantic fluency induced by semantic interference ( p < 0.0001), and (6) the highest decrease in all types of fluency induced by phonological interference ( p < 0.0001). In terms of derived indices, (7) speed interference decreased switching without affecting clustering ( p < 0.0001) and (8) phonological interference mainly affected the first time interval, whereas speed and flexibility interference primarily affected the last time interval ( p < 0.0001, all). Discussion These results, based on an interference design, indicate that letter and semantic fluency involve output lexico-phonological and semantic processes with which the strategic search process interacts, as well as an attentional component necessary to accelerate overall processing. These results also highlight interactions with other executive processes, such as those involved in stimulus dimension alternation, which require further analysis. They support our model and provide information concerning derived indices. The commonly claimed associations of executive function with switching and of semantic ability with clustering are only partially supported by our results. Finally, word production appears to be modulated by different cognitive processes over time, with a prominence of the phonological output lexicon in early production and more demanding processing (i.e., executive functioning) in late production.