We report the results of a new analysis of the ROSAT Wide Field Camera (WFC
) all-sky survey data, designed to detect extragalactic sources of extreme
ultraviolet (EW) radiation in regions of low Galactic N-H. We identify a to
tal of 19 active galactic nuclei (AGN), more than double the number of conf
irmed AGN in the published WFC (2RE) survey. Our sample contains eight narr
ow-line Seyfert 1 galaxies, making this the first reasonably sized, complet
e sample of these extreme AGN, along with six broad-line Seyfert 1s and fiv
e BL Lacertae objects. These EUV-selected sources typically have steep soft
X-ray spectra with a mean power-law energy index alpha(X) approximate to -
2. The derived AGN luminosity function is rather flat and appears to cut of
f above a luminosity of 10(46) erg s(-1) kev(-1), measured monochromaticall
y at 200 eV. Narrow-line Seyfert Is account for roughly half of the local (
z approximate to 0) volume emissivity in the EW band.