We report a measurement of the D0 and D+ lifetimes using D0→K-π+ and D+→K-π+π+ decays reconstructed in e+e-→cc¯ data recorded by the Belle II experiment at the SuperKEKB asymmetric-energy e+e- collider. The data, collected at center-of-mass energies at or near the (4S) resonance, correspond to an integrated luminosity of 72 fb-1. The results, τ(D0)=410.5±1.1(stat)±0.8(syst) fs and τ(D+)=1030.4±4.7(stat)±3.1(syst) fs, are the most precise to date and are consistent with previous determinations. © 2021 authors.