A measurement is performed of the cross section of top quark pair production in association with a W or Z boson using proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb−1, collected by the CMS experiment in 2016. The measurement is performed in the same-sign dilepton, three- and four-lepton final states. The production cross sections are measured to be σ(tt⎯⎯W)=0.77+0.12−0.11(stat)+0.13−0.12(syst)pb and σ(tt⎯⎯Z)=0.99+0.09−0.08(stat)+0.12−0.10(syst)pb. The expected (observed) signal significance for the tt⎯⎯W production in same-sign dilepton channel is found to be 4.5 (5.3) standard deviations, while for the tt⎯⎯Z production in three- and four-lepton channels both the expected and the observed significances are found to be in excess of 5 standard deviations. The results are in agreement with the standard model predictions and are used to constrain the Wilson coefficients for eight dimension-six operators describing new interactions that would modify tt⎯⎯W and tt⎯⎯Z production.