  We report the operation of a $^{87}$Rb maser in the self-oscillating mode,
using a laser diode as the optical pumping source. The maser uses a TE$_{021}$
cavity surrounding a cell containing the atoms and 11 Torr of N$_{2}$ as the
buffer gas. The optical pumping is accomplished by using a commercial laser
diode frequency-locked on the linear absorption line of an external rubidium
cell. The maser output power is maximized when the laser spectrum is spread by
modulating its frequency through the variation of its injection current. The
maser output power is also presented for various modulation waveforms and
frequencies. We find that the spurious sidebands induced by the modulation can
be minimized. Finally, the linear dependence between the laser and maser
frequencies is shown. We find that the relative maser frequency pulling from
the laser is about $4.6 \times 10^{-3}$.
