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We report improved measurements of branching fractions for charmless hadronic two-body B meson decays containing an $\ensuremath{\omega}$ meson in the final state. The results are based on a data sample of $78{\mathrm{fb}}^{\ensuremath{-}1}$ collected on the $\ensuremath{\Upsilon}(4S)$ resonance by the Belle detector. We measure the branching fractions $\mathcal{B}{(B}^{+}\ensuremath{\rightarrow}\ensuremath{\omega}{K}^{+}{)=(6.5}_{\ensuremath{-}1.2}^{+1.3}\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}{(B}^{+}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{+}{)=(5.7}_{\ensuremath{-}1.3}^{+1.4}\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ We give 90% confidence upper limits for $\mathcal{B}{(B}^{0}\ensuremath{\rightarrow}\ensuremath{\omega}{K}^{0})&lt;7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}{(B}^{0}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0})&lt;1.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ We also obtain the partial rate asymmetries ${\mathcal{A}}_{\mathrm{CP}}{=0.06}_{\ensuremath{-}0.18}^{+0.21}\ifmmode\pm\else\textpm\fi{}0.01$ for ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\omega}{K}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\mathcal{A}}_{\mathrm{CP}}{=0.50}_{\ensuremath{-}0.20}^{+0.23}\ifmmode\pm\else\textpm\fi{}0.02$ for ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}.$