Norway’s liberal abortion law allows for abortion on social indications, yet access to screening for fetal abnormalities is restricted. Norwegian regulation of, and public discourse about prenatal screening and diagnosis has been exceptional. In this study, we wanted to investigate whether the exceptional regulation is mirrored in public attitudes. An electronic questionnaire with 11 propositions about prenatal screening and diagnosis was completed by 1617 Norwegian adults (response rate 8.5%). A majority of respondents supports increased access to prenatal screening with ultrasound (60%) and/or full genome sequencing of fetal DNA (55%) available for all pregnant women. Significant minorities indicate, however, that a public offer of prenatal screening for all pregnant women would signal that people with Down syndrome are unwanted (46%) or could be criticized for contributing to a ‘sorting society’ (48%). Results indicate deeper ambivalences and a cultural sensitivity to the ethical challenges of prenatal screening and subsequent abortions. The specific diagnosis of Down syndrome and the fear of becoming a ‘sorting society’ which sorts human life due to diagnoses, appear to play prominent roles in citizen deliberations. The low response rate means that a non-response bias cannot be excluded, yet reasons why results are still likely to be of value are discussed.