A report of initial findings from an inquiry by Edinburgh City Council into the scandal at Mortonhall Crematorium has called for them to be given full access to the records once a second investigation is completed.
The inquiry was launched after child bereavement charity Sands Lothians discovered the council-owned crematorium had failed to pass on children's remains for 45 years.
The council is also to carry out a review of current policy, equipment and staff training at the crematorium to ensure national guidelines are being followed, while independent auditors from PricewaterhouseCoopers will look through more than 100,000 records at the site.
The council's chief executive, Sue Bruce, will continue to inform ministers of any issues arising from the investigation which may have national significance.
The report also recommends that an independent figure be appointed to complete the inquiry.
Councillor Lesley Hinds, environment convener, said: "Having received these findings I feel it is only right and proper, and taking into account the views of parents, that an independent person now completes the inquiry. This person would also look at all the recommendations in the report which include ensuring the council has clear policies in relation to cremations and that they comply with national guidelines."