The Hayabusa2 spacecraft collected samples from the surface of the carbonaceous near-Earth asteroid (162173) Ryugu and brought them to Earth. The samples were expected to contain organic molecules, which record processes that occurred in the early Solar System. We analyzed organic molecules extracted from the Ryugu surface samples. We identified a variety of molecules containing the atoms CHNOS, formed by methylation, hydration, hydroxylation, and sulfurization reactions. Amino acids, aliphatic amines, carboxylic acids, polycyclic aromatic hydrocarbons, and nitrogen-heterocyclic compounds were detected, which had properties consistent with an abiotic origin. These compounds likely arose from an aqueous reaction on Ryugu's parent body and are similar to the organics in Ivuna-type meteorites. These molecules can survive on the surfaces of asteroids and be transported throughout the Solar System.