Nuclides synthesized in massive stars are ejected into space via stellar winds and supernova explosions. The solar system (SS) moves through the interstellar medium and collects these nucleosynthesis products. One such product is 60Fe, a radionuclide with a half-life of 2.6 My that is predominantly produced in massive stars and ejected in supernova explosions. Extraterrestrial 60Fe has been found on Earth, suggesting close-by supernova explosions ∼2 to 3 and ∼6 Ma. Here, we report on the detection of a continuous interstellar 60Fe influx on Earth over the past ∼33,000 y. This time period coincides with passage of our SS through such interstellar clouds, which have a significantly larger particle density compared to the local average interstellar medium embedding our SS for the past few million years. The interstellar 60Fe was extracted from five deep-sea sediment samples and accelerator mass spectrometry was used for single-atom counting. The low number of 19 detected atoms indicates a continued but low influx of interstellar 60Fe. The measured 60Fe time profile over the 33 ky, obtained with a time resolution of about ±9 ky, does not seem to reflect any large changes in the interstellar particle density during Earth’s passage through local interstellar clouds, which could be expected if the local cloud represented an isolated remnant of the most recent supernova ejecta that traversed the Earth ∼2 to 3 Ma. The identified 60Fe influx may signal a late echo of some million-year-old supernovae with the 60Fe-bearing dust particles still permeating the interstellar medium.