A search for the decays Bs0→e+e- and B0→e+e- is performed using data collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to integrated luminosities of 1, 2, and 2 fb-1, respectively. No signal is observed. Assuming no contribution from B0→e+e- decays, an upper limit on the branching fraction B(Bs0→e+e-)<9.4(11.2)×10-9 is obtained at 90(95)% confidence level. If no Bs0→e+e- contribution is assumed, a limit of B(B0→e+e-)<2.5(3.0)×10-9 is determined at 90(95)% confidence level. These upper limits are more than one order of magnitude lower than the previous values.