Mini-EUSO is part of the JEM-EUSO program and operates on board the International Space Station (ISS). It is a UV-telescope with single-photon counting capability looking at nighttime downwards to the Earth through a nadir-facing UV-transparent window. As part of the pre-flight tests, the Mini-EUSO engineering model, a telescope with 1/9 of the original focal surface and a lens of 2.5 cm diameter, has been built and tested. Tests of the Mini-EUSO engineering model have been made in laboratory and in open-sky conditions. Laboratory tests have been performed at the TurLab facility, located at the Physics Department of the University of Turin, equipped with a rotating tank containing different types of materials and light sources. In this way, the configuration for the observation of the Earth from space was emulated, including the Mini-EUSO trigger schemes. In addition to the qualification and calibration tests, the Mini-EUSO engineering model has also been used to evaluate the possibility of using a JEM-EUSO-type detector for applications such as observation of space debris. Furthermore, observations in open-sky conditions allowed the studies of natural light sources such as stars, meteors, planets, and artificial light sources such as airplanes, satellites reflecting the sunlight, and city lights. Most of these targets could be detected also with Mini-EUSO. In this paper, the tests in laboratory and in open-sky conditions are reported, as well as the obtained results. In addition, the contribution that such tests provided to foresee and improve the performance of Mini-EUSO on board the ISS is discussed.