We focus on two repeating fast radio bursts (FRBs) recently detected by the CHIME/FRB experiment in 2018--2019 (Source 1: 180916.J0158+65, and Source 2: 181030.J1054+73). These sources have low excess dispersion measures (DMs) ($ < 100 rm , pc , cm^{-3}$ and $ < 20 rm , pc , cm^{-3}$, respectively), implying relatively small maximal distances. They were repeatedly observed by AGILE in the MeV--GeV energy range. We do not detect prompt emission simultaneously with these repeating events. This search is particularly significant for the submillisecond and millisecond integrations obtainable by AGILE. The sources are constrained to emit a MeV-fluence in the millisecond range below $F_{MeV} = 10^{-8} , rm erg , cm^{-2}$ corresponding to an isotropic energy near $E_{MeV,UL} simeq 2 times 10^{46},$erg for a distance of 150 Mpc (applicable to Source 1). We also searched for $gamma$-ray emission for time intervals up to 100 days, obtaining 3$,sigma$ upper limits (ULs) for the average isotropic luminosity above 50 MeV, $L_{gamma,UL} simeq ,$(5-10)$,times 10^{43} rm , erg , s^{-1}$. For a source distance near 100 kpc (possibly applicable to Source 2), our ULs imply $E_{MeV,UL}simeq10^{40} rm erg$, and $L_{gamma,UL} simeq ,$2$,times 10^{37} rm , erg , s^{-1}$. Our results are significant in constraining the high-energy emission of underlying sources such as magnetars, or other phenomena related to extragalactic compact objects, and show the prompt emission to be lower than the peak of the 2004 magnetar outburst of SGR 1806-20 for source distances less than about 100 Mpc.
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