Mitochondrial adenylate kinase with a specific GTP:AMP phosphotransferase activity (PubMed:11485571, PubMed:32822537). Could also use ITP as phosphate donor (PubMed:11485571). Its physiological function is to recycle GTP into GDP which is necessary for the TCA cycle in the mitochondrial matrix (Probable). {ECO:0000269|PubMed:11485571, ECO:0000269|PubMed:32822537, ECO:0000305|PubMed:11485571, ECO:0000305|PubMed:35457131}. This is the function of AK3 (adenylate kinase 3, Ensembl gene identifier ENSG00000147853).