There has been much debate about the origin of the diffuse γ-ray background in the MeV range. At lower energies, AGNs and Seyfert galaxies can explain the background, but not above ≃0.3 MeV. Beyond ¿10 MeV blazars appear to account for the flux observed. That leaves an unexplained gap for which different candidates have been proposed, including annihilations of WIMPS. One candidate is Type Ia supernovae (SNe Ia). Early studies concluded that they were able to account for the γ-ray background in the gap, while later work attributed a significantly lower contribution to them. All those estimates were based on SN Ia explosion models that did not reflect the full 3D hydrodynamics of SN Ia explosions. In addition, new measurements obtained since 2010 have provided new, direct estimates of high-z SN Ia rates beyond z ¿ 2. We take into account these new advances to see the predicted contribution to the gamma-ray background. We use here a wide variety of explosion models and a plethora of new measurements of SN Ia rates. SNe Ia still fall short of the observed background. Only for a fit, which would imply ¿150% systematic error in detecting SN Ia events, do the theoretical predictions approach the observed fluxes. This fit is, however, at odds at the highest redshifts with recent SN Ia rate estimates. Other astrophysical sources such as flat-spectrum radio quasars do match the observed flux levels in the MeV regime, while SNe Ia make up to 30%-50% of the observed flux.