Families connected to bereavement charity Sands want a full inquiry after their babies' remains were buried in a mass grave at Mortonhall Crematorium in Edinburgh without their knowledge and after they had been told there would be no ashes for parents to collect.
The news prompted national concerns and an investigation by The Herald revealed varying practices across Scotland.
The campaigners have now put their case to Michael Matheson, the Public Health Minister.
An independent legal expert is to be appointed to head the Edinburgh City Council-led probe in to the scandal amid continuing calls that practices all over the country should be examined. Dorothy Maitland, of Sands, said a separate public inquiry unconnected to the council was the ultimate aim, adding: "The meeting went well. We have to see what the outcome of the (council) investigation is first, but a lot of parents feel that (a public inquiry) is the only way we will get all the answers, so we are still collecting signatures for that in the meantime."
An online petition calling for a public inquiry now has 3476 names.