  (2+1)-regular static black hole solutions with a nonlinear electric field are
derived. The source to the Einstein equations is an energy momentum tensor of
nonlinear electrodynamics, which satisfies the weak energy conditions and in
the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class
of solutions is regular; the metric, curvature invariants and electric field
are regular everywhere. The metric becomes, for a vanishing parameter, the
(2+1)-static charged BTZ solution. A general procedure to derive solutions for
the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the
electric field is formulated; for relevant electric fields one requires the
fulfillment of the weak energy conditions.
