The 1991 ROSAT PSPC M 31 X-ray point source catalog has been screened in order to set up a sample of candidate supersoft sources in this galaxy, additional to the 16 supersoft sources already known in M 31 (Supper et al.,
1997A&A...317..328S). Selection criteria used were based on hardness ratios (``X-ray colors''), as developed in an earlier paper (Kahabka,
1998A&A...332..189K). An additional criterion to be fulfilled was that the observed count rate is in agreement with the expected steady-state luminosity for a source with these hardness ratios. This condition constrained mainly the hydrogen absorbing column towards the source. 26 candidates not correlating with foreground stars and M 31 supernova remnants have been found to fulfil one of the selection criteria. They can be considered to be candidate supersoft sources in M 31. This comprises 6% of all point sources in this galaxy. For these candidates absorbing hydrogen column densities, effective temperatures and white dwarf masses (assuming the sources are on the stability line of surface nuclear burning) are derived. An observed white dwarf mass distribution is derived which indicates that the masses are constrained to M>0.90M
☉. The entire population of supersoft sources in M 31 is estimated taking a theoretical white dwarf mass distribution into account and under the assumption that the observationally derived sample is restricted to white dwarf masses above 0.90M
☉. Taking into account that the gas and the source population have different scale heights a total number of at least 200-500 and at most 6,000-15,000 sources is deduced (depending on the used galaxy N
H model), making use of the population synthesis calculation of Yungelson et al. (
1996ApJ...466..890Y). The spatial distribution favors a disk (or spiral-arm) dominated young stellar population with a ratio of 1/(4-7) of bulge/disk systems, very similar to what has been found for novae in the Milky Way but lower than favored for novae in M 31 (∼1/2). Supersoft sources and Cepheids both show association with the M 31 spiral arms and may belong to a younger stellar population. A mean space density of ~(0.1-5)x10
–8pc
–3 is inferred for the supersoft sources. Assuming that all supersoft sources with masses in excess of 0.5M
☉ are progenitors of supernovae of type Ia, a SN Ia rate of (0.8-7)x10
–3yr
–1 is derived for M 31 based on these progenitors. Supersoft sources might be able to account for 20-100% of the total SN Ia rate in a galaxy like M 31.