The origin of the proton-rich trans-iron isotopes in the solar system is still uncertain. Single-degenerate thermonuclear supernovae (SNIa) with n-capture nucleosynthesis seeds assembled in the external layers of the progenitors rapidly accreting white dwarf phase may produce these isotopes. We calculate the stellar structure of the accretion phase of five white dwarf models with initial masses >~ 0.85Msun using the stellar code MESA. The near-surface layers of the 1, 1.26, 1.32 and 1.38Msun models are most representative of the regions in which the bulk of the p nuclei are produced during SNIa explosions, and for these models we also calculate the neutron-capture nucleosynthesis in the external layers. Contrary to previous rapidly-accreting white dwarf models at lower mass, we find that the H-shell ashes are the main site of n-capture nucleosynthesis. We find high neutron densities up to several 10^15 cm^-3 in the most massive WDs. Through the recurrence of the H-shell ashes these intermediate neutron densities can be sustained effectively for a long time leading to high neutron exposures with a strong production up to Pb. Both the neutron density and the neutron exposure increase with increasing the mass of the accreting WD. Finally, the SNIa nucleosynthesis is calculated using the obtained abundances as seeds. We obtain solar to super-solar abundances for p-nuclei with A>96. Our models show that SNIa are a viable p-process production site.
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