  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 $D \to \omega \pi
\pi$ to be $\mathcal{B}(D^0 \to \omega \pi^+\pi^-) = (1.33 \pm 0.16 \pm
0.12)\times 10^{-3}$ and $\mathcal{B}(D^+ \to \omega \pi^+\pi^0) =(3.87 \pm
0.83 \pm 0.25)\times 10^{-3}$, where the first uncertainties are statistical
and the second ones systematic. The statistical significances are $12.9\sigma$
and $7.7 \sigma$, respectively. The precision of $\mathcal{B}(D^0 \to \omega
\pi^+\pi^-)$ is improved by a factor of 2.1 over the CLEO measurement, and
$\mathcal{B}(D^+ \to \omega \pi^+\pi^0)$ is measured for the first time. No
significant signal of $\mathcal{B}(D^0 \to \omega \pi^0\pi^0)$ is observed, and
the upper limit on the branching fraction is $\mathcal{B}(D^0 \to \omega
\pi^0\pi^0) < 1.10 \times 10^{-3}$ at the $90\%$ confidence level. The
branching fractions of $D\to \eta \pi \pi$ are also measured and consistent
with existing results.
