We study process of dielectronic recombination with He-like uranium initially being in one of the metastable states [(1s2s)0 and (1s2p1/2)0]. We consider resonant regions of the incident electron energy corresponding to participation of triply excited states of Li-like uranium. The total and differential cross sections for dielectronic recombination as well as the energies and widths of the autoionizing states are calculated accurately within the QED theory. The cross section of the considered process is comparable in order of magnitude with the cross section of dielectronic recombination with H-like or He-like uranium initially being in the ground states. We investigated the contribution of the Breit interaction to the cross section; in particular, we found that the Breit interaction may both significantly increase and decrease the cross section.