Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40–1,000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac equation without the partial-wave expansion for the potential of two nuclei. The one-electron one-loop QED contributions (self-energy and vacuum polarization) to the ground-state energy are evaluated using the monopole approximation for the two-center potential. Interelectronic interaction of the first and second order is taken into account for the two-electron quasimolecule. Within the QED approach, one-photon-exchange contribution is calculated in the two-center potential, whereas the two-photon-exchange contribution is treated in the monopole approximation.