E3 ubiquitin-protein ligase required for accumulation of repair proteins to sites of DNA damage. Acts with ube2n/ubc13 to amplify the rnf8-dependent histone ubiquitination. Recruited to sites of DNA damage at double-strand breaks (DSBs) by binding to ubiquitinated histone H2A and ubiquitinates histone H2A and H2AX, leading to amplify the rnf8-dependent H2A ubiquitination and promoting the formation of 'Lys-63'-linked ubiquitin conjugates. This leads to concentrate ubiquitinated histones H2A and H2AX at DNA lesions to the threshold required for recruitment of tp53bp1 and brca1. Catalyzes monoubiquitination of 'Lys-13' and 'Lys-15' of nucleosomal histone H2A (H2AK13Ub and H2AK15Ub, respectively). S-ubiquitinyl-[E2 ubiquitin-conjugating enzyme]-L-cysteine + [acceptor protein]-L-lysine = [E2 ubiquitin-conjugating enzyme]-L-cysteine + N(6)-ubiquitinyl-[acceptor protein]-L-lysine. Protein modification; protein ubiquitination. Monomer. Localizes to double-strand breaks (DSBs) sites of DNA damage. The MIU motif (motif interacting with ubiquitin) mediates the interaction with both 'Lys-48'- and 'Lys-63'-linked ubiquitin chains. The UMI motif mediates interaction with ubiquitin with a preference for 'Lys-63'-linked ubiquitin. The specificity for different types of ubiquitin is mediated by juxtaposition of ubiquitin-binding motifs (MIU and UMI motifs) with LR motifs (LRMs). Belongs to the RNF168 family.