  The nearby ultraluminous infrared galaxy (ULIRG) IRAS F01004$-$2237 exhibits
100-kpc scale continuum emission at radio wavelengths. The absence of extended
X-ray emission in IRAS F01004$-$2237 has suggested an active galactic nucleus
(AGN) origin for the extended radio emission, whose properties and role in
merging systems still need to be better understood. We present the results of
multi-frequency observations of IRAS F01004$-$2237 conducted by the Very Long
Baseline Array at 2.3 and 8.4 GHz. Compact 8.4-GHz continuum emission was
detected on a 1-pc scale in the nuclear region with an intrinsic brightness
temperature of $10^{8.1}$ K suggesting that the radio source is originated from
an AGN, potentially driving the extended emission. In contrast, no significant
emission was observed at 2.3 GHz, indicating the presence of low-frequency
absorption. This absorption cannot be attributed solely to synchrotron
self-absorption; alternatively, free-free absorption due to thermal plasma is
mainly at work in the spectrum. From combined perspectives, including
mid-infrared and X-ray data, the AGN is obscured in a dense environment. The
kinetic power of the nonthermal jet, as inferred from the extended emission,
can play a more important role in dispersing the surrounding medium than the
thermal outflow in IRAS F01004$-$2237. These findings hint that jet activities
in ULIRGs may contribute to AGN feedback during galaxy evolution induced by
merger events.
