By analyzing e+e− annihilation data corresponding to an integrated luminosity of 2.93 fb−1 collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first observations of the doubly Cabibbo-suppressed decays D+→ K+π0π0 and D+→ K+π0η. The branching fractions of D+→ K+π0π0 and D+→ K+π0η are measured to be (2.1 ± 0.4stat ± 0.1syst) × 10−4 and (2.1 ± 0.5stat ± 0.1syst) × 10−4 with statistical significances of 8.8σ and 5.5σ, respectively. In addition, we search for the subprocesses D+→ K*(892)+π0 and D+→ K*(892)+η with K*(892)+→ K+π0. The branching fraction of D+→ K*(892)+η is determined to be (4.4−1.5stat+1.8± 0.2syst) × 10−4, with a statistical significance of 3.2σ. No significant signal for D+→ K*(892)+π0 is found and we set an upper limit on the branching fraction of this decay at the 90% confidence level to be 5.4 × 10−4. [Figure not available: see fulltext.] © 2022, The Author(s).