  We report first measurements of $e^{+}e^{-}$ pair production in the mass
region 0.4 $<M_{ee}<$ 2.6 GeV/$c^{2}$ at low transverse momentum ($p_T<$ 0.15
GeV/$c$) in non-central Au$+$Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and
U$+$U collisions at $\sqrt{s_{NN}}$ = 193 GeV. Significant enhancement factors,
expressed as ratios of data over known hadronic contributions, are observed in
the 40-80% centrality of these collisions. The excess yields peak distinctly at
low-$p_T$ with a width ($\sqrt{\langle p^2_T\rangle}$) between 40 to 60
MeV/$c$. The absolute cross section of the excess depends weakly on centrality
while those from a theoretical model calculation incorporating an in-medium
broadened $\rho$ spectral function and radiation from a Quark Gluon Plasma or
hadronic cocktail contributions increase dramatically with increasing number of
participant nucleons. Model calculations of photon-photon interactions
generated by the initial projectile and target nuclei describe the observed
excess yields but fail to reproduce the $p^{2}_{T}$ distributions.
