Abstract: A sample of 1.69 x 10(7) fully reconstructed pi(0) -> gamma e(+)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 pi(0) -> gamma A' 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 m(A') and mixing parameter epsilon(2) is established. The obtained upper limits on epsilon(2) are more stringent than the previous limits in the mass range 9 MeV/c(2) < m(A') < 70 MeV/c(2). The NA48/2 sensitivity to the dark photon production in the K-+/- -> pi(+/-)A' decay is also evaluated.