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). Recent massive-star and supernova activity in Earth's vicinity may be traced by radionuclides with half-lives of up to 100 million years, if trapped in interstellar dust grains that penetrate the Solar System. One such radionuclide is (60)Fe (with a half-life of 2.6 million years), which is ejected in supernova explosions and winds from massive stars. Here we report that the (60)Fe signal observed previously in deep-sea crusts is global, extended in time and of interstellar origin from multiple events. We analysed deep-sea archives from all major oceans for (60)Fe deposition via the accretion of interstellar dust particles. Our results reveal (60)Fe 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 (60)Fe 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.