We report improved measurements of branching fractions for charmless hadronic two-body B meson decays containing an ω meson in the final state. The results are based on a data sample of 78 fb-1 collected on the Y(4S) resonance by the Belle detector. We measure the branching fractions B(B+→ωK+) = (6.5-1.2 +1.3±0.6) × 10-6 and B(B +→ωπ+) = (5.7-1.3 +1.4±0.6) × 10-6. We give 90% confidence upper limits for B(B0→ωK0) <7. 6×10-6 and B(B0→ωπ0)<1.9 × 10-6. We also obtain the partial rate asymmetries A CP=0.06-0.18 +0.21 ±0.01 for B ±→ωK± and ACP=0. 50-0.20 +0.23±0.02 for B ±→ωπ±. © 2004 The American Physical Society.