Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the Earth-Mars belt from 1.08 au $< a <$ 1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04-1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower `Earth-Mars belt covering $asim(1.09, 1.17)$ au, $e<0.04$, and $I<1^circ$ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the $ u_3$, $ u_4$, and $ u_6$ secular resonances contribute to long-term instability in the outer (1.17-1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth-Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the $<200$ m scale of these NEOs, we estimated the Yarkovsky drift rates in semimajor axis, and use these to estimate that primordial asteroids with a diameter of 100 km or larger in the Earth-Mars belt would likely survive. We conclude that only a few 100-km sized asteroids could have been present in the belts region at the end of the terrestrial planet formation.
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