Serguei Serykh, 43, his wife Tatiana and Mr Serykh's stepson died after falling 15 floors at the Red Road flats in the Springburn area on 7 March.
About 200 people, including charities, faith groups, unions and locals marched from the flats to George Square.
They called for an end to the "enforced removal of refugee families".
The BBC understands the Russian family, who will not be formally identified until next-of-kin have been informed, had previously been granted asylum in Canada but left after a dispute with the authorities there.
They first arrived in the UK in 2007 and had been living at the tower block at 63 Petershill Drive, which is currently let to the YMCA, since 2 February this year.
Their application to remain in the UK had recently been refused but they had not been issued with a removal order.
According to a source familiar with the case, the family had been told that they had to leave their flat in Springburn after their application was refused.
No removal order had been issued, however, and they were advised to seek help from the Scottish Refugee Council to find alternative accommodation.
The family are believed to have jumped to their deaths shortly before 0845 GMT on 7 March.
The bodies were discovered by the concierge at the tower block.
The march, which was organised by the charity Positive Action in Housing, is also calling for the immediate return of Stephanie Ovranah and her twin six-year-old sons, Joshua and Joel.
The charity said the family were detained "without warning" on 4 March at Brand Street reporting centre in Glasgow before being moved to Yarl's Wood Detention Centre in Bedfordshire.
It said the children were "terrified of being returned to Africa, which they do not know or remember".
The rally is calling for them to be returned "to their friends, neighbours and local church in Glasgow's Cranhill where they have lived for past five five years".
BBC News
