Attosecond-magnetic-field-pulse generation is investigated using numerical solutions of the time-dependent Schr\odinger equation for oriented ${{\mathrm{H}}_{2}}^{+}$ excited and ionized by intense $2\ifmmode\times\else\texttimes\fi{}{10}^{16} \mathrm{W}/{\mathrm{cm}}^{2}$ circularly polarized attosecond UV pulses. The results show that localized attosecond-magnetic-field pulses $B$ at the molecular center $(\mathbf{r}=\mathbf{0})$ decrease in intensity with increasing attosecond-pulse wavelength, following a classical model. Magnetic-field minima are obtained at a specific laser-pulse wavelength $\ensuremath{\lambda}=55$ nm, which is attributed to ionization suppression. It is found that spatially localized coherent circular electron currents and wave packets are created and induce magnetic-field minima. At $\ensuremath{\lambda}=55$ nm, coherent excitation between the ground state and Rydberg states is created, giving rise to partial Rabi oscillations in population and doublets in molecular above-threshold-ionization photoelectron energy spectra. Pulse intensities are shown to influence these effects on the attosecond time scale through population variations.