Abstract: A search for heavy neutral lepton (N) production in K+ -> e(+)N decays using the data sample collected by the NA62 experiment at CERN in 2017-2018 is reported. Upper limits of the extended neutrino mixing matrix element vertical bar U-e4 vertical bar(2) are established at the level of 10(-9) over most of the accessible heavy neutral lepton mass range 144-462 MeV/c(2), with the assumption that the lifetime exceeds 50 ns. These limits improve significantly upon those of previous production and decay searches. The vertical bar U-e4 vertical bar(2) range favoured by Big Bang Nucleosynthesis is excluded up to a mass of about 340 MeV/c(2).