Catalyzes the phosphorylation of guanosine and inosine to GMP and IMP, respectively. ATP + guanosine = ADP + GMP + H(+) ATP + inosine = ADP + H(+) + IMP Purine metabolism; IMP biosynthesis via salvage pathway; IMP from inosine: step 1/1. Purine metabolism; GMP biosynthesis via salvage pathway. Belongs to the carbohydrate kinase PfkB family.