We have obtained Hubble Space Telescope Wide Field and Planetary Camer
a 2 ultraviolet (UV) 2200 Angstrom and optical V-band images of 20 low
-luminosity active galactic nuclei, most of which are spectroscopicall
y classified as LINERs, in order to search for a possible photoionizin
g continuum. Six (30%) of the galaxies are detected in the UV. Two of
the detected galaxies (NGC 3642 and NGC 4203) have compact, unresolved
nuclear UV sources, while the remaining four UV sources (in NGC 4569,
NGC 5005, NGC 6500, and NGC 7743) are spatially extended. Combining o
ur data set with the earlier sample of Maoz et al., we find that the p
robability of detection of a nuclear UV source is greatest for galaxie
s having low internal reddening and low inclination, and we conclude t
hat dust obscuration is the dominant factor determining whether or not
a UV source is detected. Large emission-line equivalent widths and th
e presence of broad-line emission also increase the likelihood of dete
ction of nuclear UV emission. Our results suggest that the majority of
LINERs harbor obscured nuclear UV sources, which may be either accret
ion-powered active nuclei or young star clusters. Under the assumption
that the compact UV sources in NGC 3642 and NGC 4203 have nonstellar
spectra of slope f(v) proportional to v(-1) extending into the extreme
ultraviolet, the extrapolated ionizing fluxes are sufficiently strong
to photoionize the narrow-line regions of these objects. The V-band i
mages of many galaxies in our sample reveal remarkably strong dust lan
es that may be responsible for obscuring some UV sources.