Measurements of four-lepton (4ℓ, ℓ=e,μ) production cross sections at the Z resonance in pp collisions at the LHC with the ATLAS detector are presented. For dilepton and four-lepton invariant mass regions m(ℓ+ℓ(-)) > 5 GeV and 80<m(4ℓ) < 100 GeV, the measured cross sections are 76 ± 18(stat) ± 4(syst) ± 1.4(lumi) fb and 107 ± 9(stat) ± 4(syst) ± 3.0(lumi) fb at sqrt[s] = 7 and 8 TeV, respectively. By subtracting the nonresonant 4ℓ production contributions and normalizing with Z → μ(+)μ(-) events, the branching fraction for the Z boson decay to 4ℓ is determined to be (3.20 ± 0.25(stat) ± 0.13(syst)) × 10(-6), consistent with the standard model prediction.