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 mℓ+ℓ- > 5 GeV and 80 < m4ℓ < 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 √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.