  We consider an isolated electroweak monopole solution within the Standard
Model with a non-linear Born-Infeld extension of the hypercharge gauge field.
Monopole (and dyon) solutions in such an extension are regular and their masses
are predicted to be proportional to the Born-Infeld mass parameter. We argue
that cosmological production of electroweak monopoles may delay the electroweak
phase transition and make it more strongly first order for monopole masses
$M\gtrsim 9.3\cdot 10^3$ TeV, while the nucleosynthesis constraints on the
abundance of relic monopoles impose the bound $M\lesssim 2.3\cdot 10^4$ TeV.
The monopoles with a mass in this shallow range may be responsible for the
dynamical generation of the matter-antimatter asymmetry during the electroweak
phase transition.
