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 noncentral Au + Au collisions at root s(NN) = 200 GeV and U + U collisions at root 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 (root < p(T)(2)>) between 40 and 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 an 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(T)(2) distributions.