A sample of 1.69×107 fully reconstructed π0→γe+e− decay candidates collected by the NA48/2 experiment at CERN in 2003–2004 is analyzed to search for the dark photon (A′) production in the π0→γA′ decay followed by the prompt A′→e+e− decay. No signal is observed, and an exclusion region in the plane of the dark photon mass mA′ and mixing parameter ε2 is established. The obtained upper limits on ε2 are more stringent than the previous limits in the mass range 9 MeV/c2<mA′<70 MeV/c2. The NA48/2 sensitivity to the dark photon production in the K±→π±A′ decay is also evaluated.