BACKGROUND: The days immediately after birth are the most risky for human survival, yet neonatal mortality risks are generally not reported by day. Early neonatal deaths are sometimes under-reported or might be misclassified by day of death or as stillbirths. We modelled daily neonatal mortality risk and estimated the proportion of deaths on the day of birth and in week 1 for 186 countries in 2013. METHODS: We reviewed data from vital registration (VR) and demographic and health surveys for information on the timing of neonatal deaths. For countries with high-quality VR we used the data as reported. For countries without high-quality VR data, we applied an exponential model to data from 206 surveys in 79 countries (n=50,396 deaths) to estimate the proportions of neonatal deaths per day and used bootstrap sampling to develop uncertainty estimates. FINDINGS: 57 countries (n=122,757 deaths) had high-quality VR, and modelled data were used for 129 countries. The proportion of deaths on the day of birth (day 0) and within week 1 varied little by neonatal mortality rate, income, or region. 1·00 million (36.3%) of all neonatal deaths occurred on day 0 (uncertainty range 0·94 million to 1·05 million), and 2·02 million (73.2%) in the first week (uncertainty range 1·99 million to 2·05 million). Sub-Saharan Africa had the highest risk of neonatal death and, therefore, had the highest risk of death on day 0 (11·2 per 1000 livebirths); the highest number of deaths on day 0 was seen in southern Asia (n=392,300). INTERPRETATION: The risk of early neonatal death is very high across a range of countries and contexts. Cost-effective and feasible interventions to improve neonatal and maternity care could save many lives. FUNDING: Save the Children's Saving Newborn Lives programme.