A measurement of dielectron production in proton-proton (pp) collisions at root s = 13 TeV, recorded with the ALICE detector at the CERN LHC, is presented in this Letter. The data set was recorded with a reduced magnetic solenoid field. This enables the investigation of a kinematic domain at low dielectron (ee) invariant mass m(ee) and pair transverse momentum p(T,ee) that was previously inaccessible at the LHC. The cross section for dielectron production is studied as a function of m(ee), p(T,ee), and event multiplicity dNch=d.. The expected dielectron rate from hadron decays, called hadronic cocktail, utilizes a parametrization of the measured eta/pi(0) ratio in pp and proton-nucleus collisions, assuming that this ratio shows no strong dependence on collision energy at low transverse momentum. Comparison of the measured dielectron yield to the hadronic cocktail at 0.15 < m(ee) < 0.6 GeV/c(2) and for p(T,ee) < 0.4 GeV/c indicates an enhancement of soft dielectrons, reminiscent of the "anomalous" soft-photon and soft-dilepton excess in hadron-hadron collisions reported by several experiments under different experimental conditions. The enhancement factor over the hadronic cocktail amounts to 1.61 +/- 0.13(stat) +/- 0.17(syst, data) +/- 0.34osyst; cocktailTHORN in the ALICE acceptance. Acceptance-corrected excess spectra in mee and pT; ee are extracted and compared with calculations of dielectron production from hadronic bremsstrahlung and thermal radiation within a hadronic many-body approach.
