  We obtained [O III] narrow-band imaging and multi-slit MXU spectroscopy of
the blue compact dwarf (BCD) galaxy NGC 1705 with FORS2@VLT to derive chemical
abundances of PNe and H II regions and, more in general, to characterize the
properties of the ionized gas. The auroral [O III]\lambda4363 line was detected
in all but one of the eleven analyzed regions, allowing for a direct estimate
of their electron temperature. The only object for which the [O III]\lambda4363
line was not detected is a possible low-ionization PN, the only one detected in
our data. For all the other regions, we derived the abundances of Nitrogen,
Oxygen, Neon, Sulfur and Argon out to ~ 1 kpc from the galaxy center. We detect
for the first time in NGC 1705 a negative radial gradient in the oxygen
metallicity of -0.24 \pm 0.08 dex kpc^{-1}. The element abundances are all
consistent with values reported in the literature for other samples of dwarf
irregular and blue compact dwarf galaxies. However, the average (central)
oxygen abundance, 12 + log(O/H)=7.96 \pm 0.04, is ~0.26 dex lower than previous
literature estimates for NGC 1705 based on the [O III]\lambda4363 line. From
classical emission-line diagnostic diagrams, we exclude a major contribution
from shock excitation. On the other hand, the radial behavior of the emission
line ratios is consistent with the progressive dilution of radiation with
increasing distance from the center of NGC 1705. This suggests that the
strongest starburst located within the central $\sim$150 pc is responsible for
the ionization of the gas out to at least $\sim$1 kpc. The gradual dilution of
the radiation with increasing distance from the center reflects the gradual and
continuous transition from the highly ionized H II regions in the proximity of
the major starburst into the diffuse ionized gas.
