The bacterial cell division protein FtsZ from Escherichia coli has been purified with a new calcium precipitation method. The protein contains one GDP and one Mg2+ bound, it shows GTPase activity, and requires GTP and Mg2+ to polymerize into long thin filaments at pH 6.5. FtsZ, with moderate ionic strength and low Mg2+ concentrations, at pH 7.5, is a compact and globular monomer, Mg2+ induces FtsZ self-association into oligomers, which has been studied by sedimentation equilibrium over a wide range of Mg2+ and FtsZ concentrations, The oligomer formation mechanism is best described as an indefinite self-association, with binding of an additional Mg2+ for each FtsZ monomer added to the growing oligomer, and a slight gradual decrease of the affinity of addition of a protomer with increasing oligomer size. The sedimentation velocity of FtsZ oligomer populations is compatible with a linear single-stranded arrangement of FtsZ monomers and a spacing of 4 nm. It is proposed that these FtsZ oligomers and the polymers formed under assembly conditions share a similar axial interaction between monomers (like in the case of tubulin, the eukaryotic homolog of FtsZ). Similar mechanisms may apply to FtsZ assembly in vivo, but additional factors, such as macromolecular crowding, nucleoid occlusion, or specific interactions with other cellular components active in septation have to be invoked to explain FtsZ assembly into a division ring.