Aim: To determine the willingness of women with extremely dense breasts to undergo breast cancer screening with magnetic resonance imaging (MRI) in a research setting, and to examine reasons for women to participate or not. Materials and methods: Between 2011 and 2015, 8,061 women (50–75 years) were invited for supplemental MRI as part of the Dense Tissue and Early Breast Neoplasm Screening (DENSE) trial (ClinicalTrials.gov Identifier: NCT01315015), after a negative screening mammography in the national population-based mammography screening programme. Demographics of participants and non-participants were compared. All invitees were asked to report reasons for (non)participation. Ethical approval was obtained. Participants provided written informed consent. Results: Of the 8,061 invitees, 66% answered that they were interested, and 59% eventually participated. Participants were on average 54-years old (interquartile range: 51–59 years), comparable to women with extremely dense breasts in the population-based screening programme (55 years). Women with higher socio-economic status (SES) were more often interested in participation than women with lower SES (68% versus 59%, p<0.001). The most frequently stated reasons for non-participation were “MRI-related inconveniences and/or self-reported contraindications to MRI” (27%) and “anxiety regarding the result of supplemental screening” (21%). “Expected personal health benefit” (68%) and “contribution to science” (43%) were the most frequent reasons for participation. Conclusion: Of women invited for MRI because of extremely dense breasts, 59% participated. Common reasons for non-participation were “MRI-related inconveniences” and “anxiety regarding the result of supplemental screening”. In case of future implementation, availability of precise evidence on benefits and harms might reduce this anxiety.