Forms the heterodimeric complex core-binding factor (CBF) with CBFB. RUNX members modulate the transcription of their target genes through recognizing the core consensus binding sequence 5'-TGTGGT-3', or very rarely, 5'-TGCGGT-3', within their regulatory regions via their runt domain, while CBFB is a non-DNA-binding regulatory subunit that allosterically enhances the sequence-specific DNA-binding capacity of RUNX. The heterodimers bind to the core site of a number of enhancers and promoters, including murine leukemia virus, polyomavirus enhancer, T-cell receptor enhancers, LCK, IL3 and GM-CSF promoters (Probable). May be involved in the control of cellular proliferation and/or differentiation. In association with ZFHX3, up-regulates CDKN1A promoter activity following TGF-beta stimulation (By similarity). CBF complexes repress ZBTB7B transcription factor during cytotoxic (CD8+) T cell development. They bind to RUNX-binding sequence within the ZBTB7B locus acting as transcriptional silencer and allowing for cytotoxic T cell differentiation (PubMed:18258917). CBF complexes binding to the transcriptional silencer is essential for recruitment of nuclear protein complexes that catalyze epigenetic modifications to establish epigenetic ZBTB7B silencing (PubMed:23481257). Heterodimer with CBFB. RUNX3 binds DNA as a monomer and through the Runt domain. DNA-binding is increased by heterodimerization (Probable). Interacts with TLE1 and SUV39H1. The tyrosine phosphorylated form (via runt domain) interacts with SRC (via protein kinase domain). Interacts with FYN and LCK. Interacts with FOXP3. Interacts with ZFHX3. Interacts with TBX21 (PubMed:21151104). The tyrosine phosphorylated form localizes to the cytoplasm. Translocates from the cytoplasm to the nucleus following TGF-beta stimulation. A proline/serine/threonine rich region at the C-terminus is necessary for transcriptional activation of target genes. Phosphorylated on tyrosine residues by SRC. Phosphorylated by LCK and FYN (By similarity).