  Aims. We calculate the contribution to the neutrino background from the
non-jetted active galactic nuclei (AGN) population following the recent IceCube
association of TeV neutrinos with NGC 1068. Methods. We exploit our robust
knowledge of the AGN X-ray luminosity function and evolution and convert it to
the neutrino band by using NGC 1068 as a benchmark and a theoretically
motivated neutrino spectrum. Results. The resulting neutrino background up to
redshift 5 does not violate either the IceCube diffuse flux or the upper bounds
for non-jetted AGN, although barely so. This is consistent with a scenario
where the latter class makes a substantial contribution mostly below 1 PeV,
while jetted AGN, i.e. blazars, dominate above this energy, in intriguing
agreement with the dip in the neutrino data at ~ 300 TeV. More and better
IceCube data on Seyfert galaxies will allow us to constrain the fraction of
neutrino emitters among non-jetted AGN.
