By analyzing 2.93 fb-1 of e+e- annihilation data taken at the center-of-mass energy s=3.773 GeV with the BESIII detector, we determine the branching fractions of the inclusive decays D+→φX and D0→φX to be (1.135±0.034±0.031)% and (1.091±0.027±0.035)%, respectively, where X denotes any possible particle combination. The first uncertainties are statistical, and the second are systematic. We also determine the branching fractions of the decays D→φX and their charge conjugate modes D→φX separately for the first time, and no significant CP asymmetry is observed. © 2019 authors. Published by the American Physical Society.