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Background Perinatal audit and the three-delays model are increasingly being employed to analyse barriers to perinatal health, at both community and facility level. Using these approaches, our aim was to assess factors that could contribute to perinatal mortality and potentially avoidable deaths at Rwandan hospitals. Methods Perinatal audits were carried out at two main urban hospitals, one at district level and the other at tertiary level, in Kigali, Rwanda, from July 2012 to May 2013. Stillbirths and early neonatal deaths occurring after 22 completed weeks of gestation or more, or weighing at least 500 g, were included in the study. Factors contributing to mortality and potentially avoidable deaths, considering the local resources and feasibility, were identified using a three-delays model. Results Out of 8424 births, there were 269 perinatal deaths (106 macerated stillbirths, 63 fresh stillbirths, 100 early neonatal deaths) corresponding to a stillbirth rate of 20/1000 births and a perinatal mortality rate of 32/1000 births. In total, 250 perinatal deaths were available for audit. Factors contributing to mortality were ascertained for 79% of deaths. Delay in care-seeking was identified in 39% of deaths, delay in arriving at the health facility in 10%, and provision of suboptimal care at the health facility in 37%. Delay in seeking adequate care was commonly characterized by difficulties in recognising or reporting pregnancy-related danger signs. Lack of money was the major cause of delay in reaching a health facility. Delay in referrals, diagnosis and management of emergency obstetric cases were the most prominent contributors affecting the provision of appropriate and timely care by healthcare providers. Half of the perinatal deaths were judged to be potentially avoidable and 70% of these were fresh stillbirths and early neonatal deaths. Conclusions Factors contributing to delays underlying perinatal mortality were identified in more than three-quarters of deaths. Half of the perinatal deaths were considered likely to be preventable and mainly related to modifiable maternal inadequate health-seeking behaviours and intrapartum suboptimal care. Strengthening the current roadmap strategy for accelerating the reduction of maternal and neonatal morbidity and mortality is needed for improved perinatal survival. Electronic supplementary material The online version of this article (doi:10.1186/s12884-017-1269-9) contains supplementary material, which is available to authorized users.