•Assurance enhances the credibility and transparency of sustainability reporting.•The assurance demand is greater in countries at a stage with a strong legal system and culture and in companies experiencing strong pressure from their industry.•Sustainability assurance derives from coercive, normative and mimetic isomorphism.•Normative pressure is the institutional factor that exerts the greatest explanatory power in the assurance demand. This study offers an opportunity to understand how country- and industry-specific effects may affect the decision to assure sustainability reports by identifying institutional pressures. Based on neo-institutional theory, the aim of this research is to highlight whether assurance derives from the coercive, normative and mimetic forces related to legal and cultural strength and the industry pressure for assurance, respectively. The panel data analysis of an international sample of 696 companies for the period 2007–2014 shows that voluntary assurance acts as a legitimization tool implemented by companies in response to normative, coercive and mimetic pressures; that is, companies operating in countries that have a greater legal system and cultural development, especially in industries that are greatly concerned about sustainability, are more likely to issue an assurance statement. Moreover, through a two-stage logit model, we respond to the question of which is the relevant institutional factor that causes voluntary assurance to be adopted. Specifically, we evidence that the normative factor is the one that exerts the greatest explanatory power in the assurance demand, followed by coercive pressure.