Intramolecular electronic dynamics and tunnel ionization of ${\mathrm{H}}_{2}$ in an intense laser field $(I\ensuremath{\approx}{10}^{14}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ and $\ensuremath{\lambda}=760\mathrm{nm})$ are examined with accurate evaluation of three-dimensional two-electron wave-packet dynamics by the dual transformation method. We estimated the ionization probabilities at different values of the internuclear distance R and found that tunnel ionization of ${\mathrm{H}}_{2}$ is enhanced by field-induced two-electron dynamics. An ionic component characterized by the electronic structure ${\mathrm{H}}^{+}{\mathrm{H}}^{\ensuremath{-}}$ or ${\mathrm{H}}^{\ensuremath{-}}{\mathrm{H}}^{+}$ is created near the descending well, where the dipole interaction energy with the laser electric field $\ensuremath{\varepsilon}(t)$ becomes lower. Ionization proceeds via the formation of a localized ionic component in the descending well, in contrast to the ${\mathrm{H}}_{2}^{+}$ case, in which the electron is ejected most easily from the ascending well. As R increases, while the population of ${\mathrm{H}}^{\ensuremath{-}}{\mathrm{H}}^{+}$ (or ${\mathrm{H}}^{+}{\mathrm{H}}^{\ensuremath{-}})$ decreases, a pure ionic state ${\mathrm{H}}^{\ensuremath{-}}{\mathrm{H}}^{+}$ becomes easier to ionize in an intense field because of the smallar attractive force of the distant nucleus. As a result, ionization is enhanced at the critical distance ${R}_{c}=(4\char21{}{6)a}_{0}$ ${(a}_{0}$ is the Bohr radius). Although the rate of direct ionization from a covalent state is much smaller than that from an ionic state, the ionization at large R $(g~{8a}_{0})$ mainly proceeds from the remaining covalent component, which outmeasures the created ionic component. Thus, the field-induced intramolecular electron transfer between nuclei, which triggers strong electron-electron correlation, is governed by the molecular structure as well as the field intensity. The mechanism of the ionization enhanced by field-induced intramolecular electron transfer is consistent with the observation of charge-asymmetric dissociation channels of diatomic molecules such as ${\mathrm{N}}^{+}+{\mathrm{N}}^{3+}.$ We also investigated the intramolecular electronic dynamics by analyzing the populations of field-following adiabatic states defined as eigenfunctions of the instantaneous electronic Hamiltonian. An effective instantaneous Hamiltonian for ${\mathrm{H}}_{2}$ was constructed of three main electronic states, X, $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ and $\mathrm{EF}.$ We found that the difference in electronic and ionization dynamics between the small R and large R cases originates in the character of the level crossing of the lowest two adiabatic states.