It follows the publication of a report yesterday that shows staff at a Edinburgh crematorium buried baby ashes in secret for decades. Parents were told there were no ashes left when young babies were cremated at Mortonhall Crematorium.
The report by Dame Elish Angiolini described the practice as a "great tragedy" that left some parents facing a "lifetime of uncertainty". The families of more than 250 dead babies were affected by the scandal.
Dame Elish, a former Lord Advocate, said managers at the council-run crematorium knew that ashes were left after babies were cremated. But parents were not told as managers believed it would have been "too distressing" for them.
Cheryl Buchanan, 33, from Barlanark, is among a group of mothers in Glasgow calling for a public inquiry. The group, Glasgow Answers For Ashes, is also planning to launch a petition calling on Glasgow City Council to launch its own investigation into historical practices.
Cheryl's daughter Taylor died in the womb in 2004.
A funeral was arranged for Taylor, who was cremated at Daldowie Crematorium, Uddingston, in a white coffin. But when Cheryl phoned the crematorium to find out about collecting Taylor's ashes, she was told there were none.
The council reported 2385 cremations were carried out at Linn and Daldowie during this time and in 1886 cases no remains were recovered.
Cheryl said: "I read Dame Elish's report and am appalled by the things I have read. Whatever has been happening there, has probably been happening all over Scotland."
A Glasgow council spokesman said: "The council still believes the Scottish Government should commission an independent nationwide inquiry with the power to examine individual cases."