An off-line scan for nontriggered gamma-ray bursts (GRBs) in the BATSE dail
y records at 1024 ms time resolution covering about 7 yr of observations ga
ve 1353 nontriggered and 1581 triggered GRBs. The scan efficiency was measu
red by adding artificial test bursts to the data. The log N- log P distribu
tion could be extended down to peak fluxes, P similar to 0.1 photons cm(-2)
s(-1). Previous indications of a turnover at small P are not confirmed. Th
e log N- log P distribution cannot be fitted with a standard candle model w
ith a nonevolving GRB source population, assuming that there are no large n
on-GRB contaminations. It is likely that the intrinsic luminosity function
of GRBs is wide.