Processing of organic molecules by liquid water was probably an essential requirement towards the emergence of terrestrial primitive life. According to Oparin's hypothesis, organic building blocks required for early life were produced from simple organic molecules formed in a primitive reducing atmosphere. Geochemists favour now a less reducing atmosphere dominated by carbon dioxide. In such an atmosphere, very few building blocks are formed. Import of extraterrestrial organic molecules may represent an alternative supply. Experimental support for such an alternative scenario is examined in comets, meteorites and micrometeorites. The early histories of Mars and Earth clearly show similarities. Liquid water was once stable on the surface of Mars attesting the presence of an atmosphere capable of decelerating C-rich micro-meteorites. Therefore, primitive life may have developed on Mars, as well. Liquid water disappeared from the surface of Mars very early, about 3.8 Ga ago. The Viking missions did not find, at the surface of the Martian soil, any organic molecules or clear-cut evidence for microbial activities such as photosynthesis, respiration or nutrition. The results can be explained referring to an active photochemistry of Martian soil driven by the high influx of solar UV. These experiments do not exclude the existence of organic molecules and fossils of micro-organisms which developed on early Mars until liquid water disappeared. Mars may store below its surface some well preserved clues of a still hypothetical primitive life.