We present a generalization of the semiclassical theory of tunneling of electrons from deeply bound states in highly charged ions subject to a static electromagnetic field of extreme strength [J. Exp. Theor. Phys. 87, 433 (1998)] to the case where the electric and magnetic fields are of an arbitrary relative amplitude and directed at an arbitrary angle. The obtained result accounts for the Coulomb interaction and spin precession. Derived formulas can be used for the calculation of ionization rates in tightly focused laser pulses of multipetawatt and exawatt power. We demonstrate application of the rates for the analysis of tunnel ionization of H-like ions of xenon and radon at intensities above ${10}^{24}\mathrm{W}/{\mathrm{cm}}^2$.

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• Multiphoton or tunneling ionization & excitation
• Strong electromagnetic field effects