As the possibility of implementing population genomic screening programs for the risk of developing hereditary cancers in health systems increases, understanding how to support individuals who wish to have genomic screening is essential. This qualitative study aimed to link public perceived barriers to a) taking up the offer of population genomic screening for breast or prostate cancer risk and b) taking up risk-management options following their result, with possible theory-informed behaviour-change approaches that may support implementation. Ten focus groups were conducted with a total of 25 members of the Australian public to identify and then categorise barriers within the behaviour-change Capability, Opportunity, Motivation - Behaviour (COM-B) model. Ten COM-B categorised barriers were identified as perceived influences on an individual's intentions to take-up the offer, including Capability (e.g., low public awareness), Opportunity (e.g., inconvenient sample collection procedure) and Motivation (e.g., genomic screening not perceived as relevant to an individual). Ten barriers for taking up risk-management options included Motivation (e.g., concerns about adverse health impact) and Opportunity (e.g., social opportunity and cost incurred to the individual). Our findings demonstrate that a nuanced approach is required to support people to take-up the offer of population genomic screening and, where appropriate, to adopt risk-management options. Even amongst participants who were enthusiastic about a population genomic screening program, needs were varied, demanding a range of implementation strategies. Promulgating equitable uptake of genomic screening and management options for breast and prostate cancer risk will require a needs-based approach.