Catalyzes the ATP-dependent phosphorylation of thiamine-monophosphate (TMP) to form thiamine-pyrophosphate (TPP), the active form of vitamin B1. Cannot use thiamine as substrate. Is highly specific for ATP as phosphate donor. ATP + thiamine phosphate = ADP + thiamine diphosphate Is markedly activated by the monovalent cations K(+), NH(4)(+), and Rb(+). Is significantly inhibited by ADP, AMP, p-chloromercuribenzoate, N-ethylmaleimide, pyrophosphate, and EDTA. Optimum pH is about 8.0. Cofactor biosynthesis; thiamine diphosphate biosynthesis; thiamine diphosphate from thiamine phosphate: step 1/1. Reaction mechanism of ThiL seems to utilize a direct, inline transfer of the gamma-phosphate of ATP to TMP rather than a phosphorylated enzyme intermediate. Belongs to the thiamine-monophosphate kinase family.