The rate of supernovae in our local Galactic neighbourhood within a distance of about 100 parsecs from Earth is estimated to be one every 2-4 million years, based on the total rate in the Milky Way (2.0 +/- 0.7 per century(1,2)). Recent massive-star and supernova activity in Earth's vicinity may be traced by radionuclides with half-lives of up to 100 million years(3-6), if trapped in interstellar dust grains that penetrate the Solar System. One such radionuclide is Fe-60 (with a half-life of 2.6 million years)(7,8), which is ejected in supernova explosions and winds from massive stars(1,2,9). Here we report that the Fe-60 signal observed previously in deep-sea crusts(10,11) is global, extended in time and of interstellar origin from multiple events. We analysed deep-sea archives from all major oceans for Fe-60 deposition via the accretion of interstellar dust particles. Our results reveal Fe-60 interstellar influxes onto Earth at 1.5-3.2 million years ago and at 6.5-8.7 million years ago. The signal measured implies that a few per cent of fresh Fe-60 was captured in dust and deposited on Earth. Our findings indicate multiple supernova and massive-star events during the last ten million years at distances of up to 100 parsecs.