  This article presents a measurement of $\nu_e$ interactions without pions in
the final state using the MicroBooNE experiment and an investigation into the
excess of low-energy electromagnetic events observed by the MiniBooNE
collaboration. The measurement is performed in exclusive channels with
(1$e$N$p$0$\pi$) and without (1$e$0$p$0$\pi$) visible final-state protons using
6.86$\times 10^{20}$ protons on target of data collected from the Booster
Neutrino Beam at Fermilab. Events are reconstructed with the Pandora pattern
recognition toolkit and selected using additional topological information from
the MicroBooNE liquid argon time projection chamber. Using a goodness-of-fit
test the data are found to be consistent with the predicted number of events
with nominal flux and interaction models with a $p$-value of 0.098 in the two
channels combined. A model based on the low-energy excess observed in MiniBooNE
is introduced to quantify the strength of a possible $\nu_e$ excess. The
analysis suggests that if an excess is present, it is not consistent with a
simple scaling of the $\nu_e$ contribution to the flux. Combined, the
1$e$N$p$0$\pi$ and 1$e$0$p$0$\pi$ channels do not give a conclusive indication
about the tested model, but separately they both disfavor the low-energy excess
model at $>$90% CL. The observation in the most sensitive 1$e$N$p$0$\pi$
channel is below the prediction and consistent with no excess. In the less
sensitive 1$e$0$p$0$\pi$ channel the observation at low energy is above the
prediction, while overall there is agreement over the full energy spectrum.
