The deuteron electromagnetic form factors are calculated and their sensitivity to realistic deuteron wave functions of various realistic and high-precision NN potential models is investigated. We consider six NN potential models which are classified into local and nonlocal potentials. As local potentials, the Argonne V18, Chiral N 3LO, and Nijmegen (Nijm-II) potentials are used. For the nonlocal ones, the Bonn-Q, CD-Bonn, and Nijmegen (Nijm-I) potentials are considered. For the free nucleon form factors, the standard dipole fit for the proton and neutron form factors is used. We found that the results for deuteron form factors are slightly dependent on the NN potential model adapted for the deuteron wave function. In addition, the sensitivity of our results for deuteron form factors to the D-wave component of the deuteron wave functions is also studied. We obtained a small difference between the results with and without the D-wave contribution.