Catalyzes the reversible transfer of the terminal phosphate of ATP to form a long-chain polyphosphate (polyP). [phosphate](n) + ATP = [phosphate](n+1) + ADP An intermediate of this reaction is the autophosphorylated ppk in which a phosphate is covalently linked to a histidine residue through a N-P bond. Belongs to the polyphosphate kinase 1 (PPK1) family.