A search for the rare hadronic decay B0s→p¯p is performed using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6  fb−1. No evidence of the decay is found and an upper limit on its branching fraction is set at B(B0s→p¯p)<4.4(5.1)×10−9 at 90% (95%) confidence level; this is currently the world’s best upper limit. The decay mode B0→p¯p is measured with very large significance, confirming the first observation by the LHCb experiment in 2017. The branching fraction is determined to be B(B0→p¯p)=(1.27±0.15±0.05±0.04)×10−8, where the first uncertainty is statistical, the second is systematic and the third is due to the external branching fraction of the normalization channel B0→K+π−. The combination of the two LHCb measurements of the B0→p¯p branching fraction yields B(B0→p¯p)=(1.27±0.13±0.05±0.03)×10−8.