In order to assist the elaboration of proactive measures for the management of future volcanic eruptions in Iceland, we developed a new scenario-based approach to assess the hazard associated with tephra dispersal and sedimentation at various scales and for multiple sources. The target volcanoes are Hekla, Katla, Eyjafjallajökull and Askja, selected either for their high probabilities of eruption and/or their high potential impact. By coupling tephrostratigraphic studies, probabilistic techniques and modelling, we developed comprehensive eruption scenarios for both short- and long-lasting eruptions and compiled hazard maps for tephra ground deposition at a national scale and air concentration at a European scale using the TEPHRA2 and FALL3D models, respectively. New algorithms for the identification of realistic sets of eruptive source parameters are investigated, which assist the generation of probability density functions of eruption source parameters for the selected scenarios. Aggregation processes were accounted for using various empirical models. Outcomes, i.e. probabilities conditioned to the occurrence of an eruption, help the assessment and comparison of hazard levels at different scales. For example, at a national scale Askja has a 5–10% probability of blanketing the easternmost half of the country with a tephra accumulation of at least 1 kg m<sup>−2</sup>. At a continental scale, Katla has a 5–10% probability of producing ash clouds with concentrations of 2 mg m<sup>−3</sup> over the UK, Scandinavia and northern Europe with a mean arrival time of 48–72 h and a mean persistence time of 6–18 h. In a companion paper, Scaini et al. (2014) present a vulnerability assessment for Iceland to ground deposition of tephra and for the European air traffic to airborne ash which, combined with the outcomes of the present paper, constitute one of the first comprehensive multi-scale risk assessment associated with tephra dispersal and sedimentation.