Prestahnukur is a 570m high rhyolite glaciovolcanic edifice in Iceland's Western Rift Zone with a volume of 0.6 km3. Uniform whole rock, mineral and glass compositions suggest that Prestahnukur was constructed during the eruption of one magma batch. Ar-Ar dating gives an age of 89+/-24 ka, which implies eruption during the transition (Oxygen Isotope substages 5d to 5a) between the Eemian interglacial and the Weichselian glacial period. Prestahnukur is unique among published accounts of rhyolite tuyas because a base of magmatically-fragmented tephra appears to be absent. Instead, basal exposures consist of glassy lava lobes and coarse hyaloclastite, above which are single and multiple lava sheets with matrix-supported basal breccias and hyaloclastite upper carapaces. Steepening ramp structures at sheet termini are interpreted as ice-contact features. Interactions between erupting magma and water/ice have affected all lithologies. A preliminary model for the construction of Prestahnukur involves an effusive subglacial eruption between 2 and 19 years duration which never became emergent, into an ice sheet over 700m thick. If 700m of ice had built up during this interglacial-glacial transition, this would corroborate models arguing for the swift accumulation of land-based ice in rapid response to global cooling.