Using 2.93 fb-1 of e+e- collision data taken at a center-of-mass energy of 3.773 GeV by the BESIII detector at the BEPCII, we measure the branching fractions of the singly Cabibbo-suppressed decays D→ωππ to be B(D0→ωπ+π-)=(1.33±0.16±0.12)×10-3 and B(D+→ωπ+π0)=(3.87±0.83±0.25)×10-3, where the first uncertainties are statistical and the second ones systematic. The statistical significances are 12.9σ and 7.7σ, respectively. The precision of B(D0→ωπ+π-) is improved by a factor of 2.1 over prior measurements, and B(D+→ωπ+π0) is measured for the first time. No significant signal for D0→ωπ0π0 is observed, and the upper limit on the branching fraction is B(D0→ωπ0π0)<1.10×10-3 at the 90% confidence level. The branching fractions of D→ηππ are also measured and consistent with existing results.