The observational evidence for a population of quasars powered by supermassive black holes of mass \geq 10^9 M_sun at redshifts z\geq 6 poses a great challenge for any model describing the formation of galaxies. Assuming uninterrupted accretion at the Eddington limit, seed black holes of at least 1000 M_sun are needed at z \approx 15. Here I study whether these seeds could be primordial black holes (PBHs) which have been produced in the very early universe by the collapse of primordial density fluctuations. In particular, I study the expected number densities of PBHs in the relevant mass range for several classes of spectra of primordial density fluctuations and confront the results with observational data. While it seems to be possible to produce the required PBHs with spectra showing large enhancements of fluctuations on a certain scale, our hypothesis can be clearly disproved for a scale free spectrum of primordial fluctuations described by a power-law slope consistent with recent observations.

9 pages, 3 figures, minor changes, references added, accepted for publication in the September 2004 issue of Phys. Rev. D