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The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in pp collisions at s√ = 5.02 TeV and p-Pb collisions at sNN−−−√ = 5.02 TeV with the ALICE detector at the LHC is reported. The D0, D+, and D∗+ mesons, together with their charge conjugates, were reconstructed at midrapidity in the transverse momentum interval 3 < pT < 24 GeV/c and correlated with charged particles having pT > 0.3 GeV/c and pseudorapidity |η|< 0.8. The properties of the correlation peaks appearing in the near- and away-side regions (for Δφ≈ 0 and Δφ≈π, respectively) were extracted via a fit to the azimuthal correlation functions. The shape of the correlation functions and the near- and away-side peak features are found to be consistent in pp and p-Pb collisions, showing no modifications due to nuclear effects within uncertainties. The results are compared with predictions from Monte Carlo simulations performed with the PYTHIA, POWHEG+PYTHIA, HERWIG, and EPOS 3 event generators.