Responsible research and innovation (RRI) approaches that have emerged in the past ten years point to the importance of engaging the public in dialogues about research. The different variants of RRI share the notion that societal actors, including citizens, need to work together – that is, engage in two-way communication during the research and innovation process – in order to better align both the process and its outcomes with the values, needs and expectations of society. Yet, sponsors and organizers of dialogues about research often face difficulties in recruiting sufficient numbers of participants or ensuring a sufficient level of diversity of participants. This paper asks what motivates or hinders individual citizens as members of the broader public to participate in such dialogues. It presents empirical findings of the European Union-funded project Promoting Societal Engagement Under the Terms of RRI (PROSO), which aimed to foster public engagement with research for RRI. PROSO used a quasi-experimental, qualitative approach directly involving citizens to address this question. The core of the innovative methodology were focus group discussions with European citizens about hypothetical opportunities to take part in dialogues about research. Three hypothetical scenarios of different dialogue formats (varied by whether they seek to inform the participants, consult or enable deeper collaboration on a scientific issue) were used as stimuli to explore the participants’ willingness (motivations and perceived barriers) to engage with scientific research. Our findings show a preference towards dialogue formats that give citizens a more active role and a greater say in research policy or research funding. They further suggest that those who seek to broaden citizen participation in dialogues about research should consider the role of relevance, impact, trust, legitimacy, knowledge, and time and resources as factors that can motivate or discourage citizens to take part. Based on our findings, we discuss possibilities to promote citizen participation in dialogues about research as part of putting RRI into practice.