The Pacific plate converges with northeastern Eurasia at a rate of 8-9 m per century along the Kamchatka, Kuril and Japan trenches. Along the southern Kuril trench, which faces the Japanese island of Hokkaido, this fast subduction has recurrently generated earthquakes with magnitudes of up to approximately 8 over the past two centuries. These historical events, on rupture segments 100-200 km long, have been considered characteristic of Hokkaido's plate-boundary earthquakes. But here we use deposits of prehistoric tsunamis to infer the infrequent occurrence of larger earthquakes generated from longer ruptures. Many of these tsunami deposits form sheets of sand that extend kilometres inland from the deposits of historical tsunamis. Stratigraphic series of extensive sand sheets, intercalated with dated volcanic-ash layers, show that such unusually large tsunamis occurred about every 500 years on average over the past 2,000-7,000 years, most recently approximately 350 years ago. Numerical simulations of these tsunamis are best explained by earthquakes that individually rupture multiple segments along the southern Kuril trench. We infer that such multi-segment earthquakes persistently recur among a larger number of single-segment events.