The Hayabusa2 spacecraft explored asteroid Ryugu and brought its surface materials to Earth. Ryugu samples resemble Ivuna-type (CI) chondrites—the most chemically primitive meteorites—and contain secondary phyllosilicates and carbonates, which are indicative of aqueous alteration. Understanding the conditions (such as temperature, redox state and fluid composition) during aqueous alteration is crucial to elucidating how Ryugu evolved to its present state, but little is known about the temporal changes in these conditions. Here we show that calcium carbonate (calcite) grains in Ryugu and Ivuna samples have variable ¹⁸O/¹⁶O and ¹³C/¹²C ratios that are, respectively, 24–46‰ and 65–108‰ greater than terrestrial standard values, whereas those of calcium–magnesium carbonate (dolomite) grains are much more homogeneous, ranging within 31–36‰ for oxygen and 67–75‰ for carbon. We infer that the calcite precipitated first over a wide range of temperatures and oxygen partial pressures, and that the proportion of gaseous CO₂/CO/CH₄ molecules changed temporally. By contrast, the dolomite formed later in a more oxygen-rich and thus CO₂-dominated environment when the system was approaching equilibrium. The characteristic isotopic compositions of secondary carbonates in Ryugu and Ivuna are not observed for other hydrous meteorites, suggesting a unique evolutionary pathway for their parent asteroid(s).