The Covid-19 pandemic affects mortality directly through infection MESHD as well as through changes in the social, environmental and healthcare determinants of health. The impacts on mortality are likely to vary across countries in magnitude, timing, and age TRANS and sex composition. Here, we applied an ensemble of 16 Bayesian probabilistic models to vital statistics data, by age group TRANS and sex, to consistently and comparably estimate the impacts of the first phase of the pandemic on all-cause mortality for 17 industrialised countries. The models accounted for factors that affect death MESHD rates including seasonality, temperature, and public holidays, as well as for medium-long-term secular trends and the dependency of death MESHD rates in each week on those in preceding week(s). From mid-February through the end of May 2020, an estimated 202,900 (95% credible interval 179,400-224,900) more people died in these 17 countries than would have had the pandemic not taken place. Nearly three quarters of these excess deaths MESHD occurred in England and Wales, Italy and Spain, where less than half of the total population of these countries live. When all-cause mortality is considered, the total number of deaths MESHD, deaths MESHD per 100,000 people, and relative increase in deaths MESHD were similar between men and women in most countries. Further, in many countries, the balance of excess deaths MESHD changed from male TRANS-dominated early in the pandemic to being equal or female TRANS-dominated later on. Taken over the entire first phase of the pandemic, there was no detectable rise in all-cause mortality in New Zealand, Bulgaria, Hungary, Norway, Denmark and Finland and for women in Austria and Switzerland (posterior probability of an increase in deaths MESHD <90%). Women in Portugal and men in Austria experienced relatively small increases in all-cause mortality, with posterior probabilities of 90-99%. For men in Switzerland and Portugal, and both sexes in the Netherlands, France, Sweden, Belgium, Italy, Scotland, Spain and England and Wales, all-cause mortality increased as a result of the pandemic with a posterior probability >99%. After accounting for population size, England and Wales and Spain experienced the highest death MESHD toll, nearly 100 deaths MESHD per 100,000 people; they also had the largest relative (percent) increase in deaths MESHD (37% (95% credible interval 30-44) in England and Wales; 38% (31-44) in Spain). New Zealand, Bulgaria, Hungary, Norway, Denmark and Finland experienced changes in deaths MESHD that ranged from possible slight declines to increases of no more than 5%. The large impact in England and Wales stems partly from having experienced (together with Spain) the highest weekly increases in deaths MESHD, more than doubling in some weeks, and having had (together with Sweden) the longest duration when deaths MESHD exceeded levels that would be expected in the absence of the pandemic. The heterogeneous magnitude and character of the excess deaths MESHD due to the Covid-19 pandemic reflect differences in how well countries have managed the pandemic (e.g., timing, extent and adherence to lockdowns and other social distancing measures; effectiveness of test, trace TRANS and isolate mechanisms), and the resilience and preparedness of the health and social care system (e.g., effective facility and community care pathways; minimising spread of infection MESHD within hospitals and care homes, and between them and the community).