Considering an electron interacting with an atomic or molecular potential and an external static electric field, one usually focuses on narrow resonances at negative energies originating from the bound states in the absence of the field; we call them tunneling states (TSs). Meanwhile, there also exist relatively broad resonances at positive energies having no counterparts in the absence of the field; we call them static-field-induced states (SFISs). In this paper, the recently developed weak-field asymptotic theory of TSs [O. I. Tolstikhin et al., Phys. Rev. A 84, 053423 (2011)] is extended to SFISs. An asymptotic quantization condition defining the energies of SFISs in an arbitrary potential in the three-dimensional case is derived. The parabolic scattering amplitudes appearing in this quantization condition are defined. The theory is illustrated by calculations for the zero-range and Coulomb potentials. The SFISs in these potentials are found and their energies are shown to be in good agreement with the asymptotic results over a wide interval of the values of the field.