Asymmetries in the time-dependent rates of D^{0}→K^{+}K^{-} and D^{0}→π^{+}π^{-} decays are measured in a pp collision data sample collected with the LHCb detector during LHC Run 1, corresponding to an integrated luminosity of 3 fb^{-1}. The asymmetries in effective decay widths between D^{0} and D[over ¯]^{0} decays, sensitive to indirect CP violation, are measured to be A_{Γ}(K^{+}K^{-})=(-0.30±0.32±0.10)×10^{-3} and A_{Γ}(π^{+}π^{-})=(0.46±0.58±0.12)×10^{-3}, where the first uncertainty is statistical and the second systematic. These measurements show no evidence for CP violation and improve on the precision of the previous best measurements by nearly a factor of two.