We investigate the formation by accretion of massive primordial protostars in the range 10 to 300 Msun. The high accretion rate used in the models (4.4 x 10^{-3} Msun/yr) causes the structure and evolution to differ significantly from those of both present-day protostars and primordial zero-age main sequence stars. After an initial expansion of the radius (for < 12 Msun), the protostar undergoes an extended phase of contraction (up to 60 Msun). The stellar surface is not visible throughout most of the main accretion phase, since a photosphere is formed in the infalling envelope. Also, significant nuclear burning does not take place until a protostellar mass of about 80 Msun. As the interior luminosity approaches the Eddington luminosity, the protostellar radius rapidly expands, reaching a maximum around 100 Msun. Changes in the ionization of the surface layers induce a secondary phase of contraction, followed by a final swelling due to radiation pressure when the stellar mass reaches about 300 Msun. This expansion is likely to signal the end of the main accretion phase, thus setting an upper limit to the protostellar mass formed in these conditions.

11 pages and 4 figures. ApJL accepted