Enabling a flexible and natural human-robot interaction (HRI) for industrial robots is a critical yet challenging task that can be facilitated by the use of conversational artificial intelligence (AI). Prior research has concentrated on strengthening interactions through the deployment of social robots, while disregarding the capabilities required to boost the flexibility and user experience associated with human-robot collaboration (HRC) on manufacturing tasks. One of the main challenges is the lack of publicly available industrial-oriented dialogue datasets for the training of conversational AI. In this work, we present an industrial robot wizard-of-Oz dialoguing dataste (IRWoZ) focused on enabling HRC in manufacturing tasks. The dataset covers four domains: assembly, transportation, position, and relocation. It is created using the Wizard-of-Oz technique to be less noisy. We manually constructed, annotated and validated dialogue segments (e.g., intentions, slots, annotations), as well as the responses. Building upon the proposed dataset, we benchmark it on the state-of-the-art (SoTA) language models, generative pretrained (GPT-2) models, on dialogue state tracking and response generation tasks. We expect that the IRWoZ dataset will facilitate exciting ongoing dialogue research and we provide it freely accessible at https://github.com/lcroy/ToD4IR/tree/main/dataset.INDEX TERMS data collection, data annotation, dialogue systems, virtual assistants, human-robot interaction.