Stars with about 45 to 80% the mass of the Sun, so-called K dwarf stars, have previously been proposed as optimal host stars in the search for habitable extrasolar worlds. These stars are abundant, have stable luminosities over billions of years longer than Sun-like stars, and offer favourable space environmental conditions. So far, the theoretical and experimental focus on exoplanet habitability has been on even less massive, though potentially less hospitable red dwarf stars. Here we present the first experimental data on the responses of photosynthetic organisms to a simulated K dwarf spectrum. We find that garden cress Lepidium sativum under K-dwarf radiation exhibits comparable growth and photosynthetic efficiency as under Solar illumination on Earth. The cyanobacterium Chroococcidiopsis sp. CCMEE 029 exhibits significantly higher photosynthetic efficiency and culture growth under K dwarf radiation compared to Solar conditions. Our findings of the affirmative responses of these two photosynthetic organisms to K dwarf radiation suggest that exoplanets in the habitable zones around such stars deserve high priority in the search for extrasolar life.