Catalyzes the phosphorylation of guanosine and inosine to GMP and IMP, respectively (PubMed:7721718, PubMed:7665468, PubMed:10879466). Can also use deoxyguanosine and xanthosine, but not adenosine, uridine, cytidine or deoxythymidine (PubMed:7665468, PubMed:10879466). Shows a strong preference for guanosine (PubMed:7665468, PubMed:10879466). dATP can serve as a phosphate donor as well as ATP. Shows weaker activity with UTP and CTP (PubMed:7665468, PubMed:10879466). ATP + guanosine = ADP + GMP + H(+) ATP + inosine = ADP + H(+) + IMP Mg(2+) is probably required for activity in addition to its role in forming the Mg-ATP complex. Guanosine and inosine kinase activities are both inhibited by ppGpp, a nucleotide messenger universally produced in bacteria following nutrient starvation. ppGpp binds to Gsk, and inhibits its activity by blocking conformational dynamics and inducing tetramerization. Inhibiting purine nucleotide synthesis is required during starvation to maintain levels of the metabolite 5'-phosphoribosyl-1'-diphosphate (pRpp), which is required for the synthesis of histidine and tryptophan (PubMed:32857952). Activity is slightly increased in the presence of pyrimidine nucleotides, while it is markedly inhibited by GDP and GTP (PubMed:10879466). Activity is stimulated by K(+) ions (PubMed:7665468). Guanosine and inosine kinase activities are inhibited by Cu(2+) or Zn(2+) (PubMed:7665468). Optimum pH is 8.2 for guanosine kinase activity. Optimum pH is 6.9 for inosine kinase activity. Optimum temperature is 38 degrees Celsius for guanosine kinase activity and between 26 and 39 degrees Celsius for inosine kinase activity. Purine metabolism; IMP biosynthesis via salvage pathway; IMP from inosine: step 1/1. Purine metabolism; GMP biosynthesis via salvage pathway. Homodimer. Disruption of the gene causes a considerable amount of guanosine accumulation together with a slight increase in the inosine productivity. Belongs to the carbohydrate kinase PfkB family.