The amount of ice present in clouds can affect cloud lifetime, precipitation and radiative properties. The formation of ice in clouds is facilitated by the presence of airborne ice-nucleating particles. Sea spray is one of the major global sources of atmospheric particles, but it is unclear to what extent these particles are capable of nucleating ice. Sea-spray aerosol contains large amounts of organic material that is ejected into the atmosphere during bubble bursting at the organically enriched sea-air interface or sea surface microlayer. Here we show that organic material in the sea surface microlayer nucleates ice under conditions relevant for mixed-phase cloud and high-altitude ice cloud formation. The ice-nucleating material is probably biogenic and less than approximately 0.2 micrometres in size. We find that exudates separated from cells of the marine diatom Thalassiosira pseudonana nucleate ice, and propose that organic material associated with phytoplankton cell exudates is a likely candidate for the observed ice-nucleating ability of the microlayer samples. Global model simulations of marine organic aerosol, in combination with our measurements, suggest that marine organic material may be an important source of ice-nucleating particles in remote marine environments such as the Southern Ocean, North Pacific Ocean and North Atlantic Ocean.