Integrated fiducial cross sections for the production of four leptons via the H -> 4l decays (l = e, mu) are measured in pp collisions at root s = 7 and 8TeV. Measurements are performed with data corresponding to integrated luminosities of 5.1 fb(-1) at 7TeV, and 19.7 fb(-1) at 8 TeV, collected with the CMS experiment at the LHC. Differential cross sections are measured using the 8 TeV data, and are determined as functions of the transverse momentum and rapidity of the four-lepton system, accompanying jet multiplicity, transverse momentum of the leading jet, and difference in rapidity between the Higgs boson candidate and the leading jet. A measurement of the Z -> 4l cross section, and its ratio to the H -> 4l cross section is also performed. All cross sections are measured within a fiducial phase space defined by the requirements on lepton kinematics and event topology. The integrated H -> 4l fiducial cross section is measured to be 0.56-(+0.67)(0.44) (stat) (+0.21)(-0.06) (syst) fb at 7 TeV, and 1.11(-0.35)(+ 0.41) (stat) (+ 0.14)(-0.10) (syst) fb at 8 TeV. The measurements are found to be compatible with theoretical calculations based on the standard model.