Students Alexander and Bridget Jones were walking on Swanston Street in Carlton on Thursday when a section of brick wall collapsed on them.
Alexander, 19, was killed, while Bridget, 18, suffered critical injuries and is fighting for her life in hospital.
Their parents Sue and Ian Jones have issued a statement saying they are devastated by the terrible circumstances surrounding their beautiful children and thanking those who helped.
"We are overwhelmed at the loss of our son Alexander and are very distressed to see our critically ill daughter in the hospital," the statement said.
"We understand people who were passing by and the emergency services did everything that they could and we are so grateful these people tried their best for our children."
They said their hearts go out to the family of the other woman, believed to be in her 30s, who was killed in the tragedy.
They also thanked police and staff and the Royal Melbourne hospital for being caring and respectful.
"We would like to thank our family and friends and the friends of Alexander and Bridget, the Montmorency Secondary College community, and many others who have sent in their wishes and offered support."
They have asked that their privacy be respected at this sad and difficult time.
Meanwhile, Melbourne's Lord Mayor Robert Doyle has called for tougher building codes, following the death of two pedestrians after a wall collapse in the city on Thursday.
A 19-year-old man and a woman in her thirties were killed at the scene when a 15-metre long section of brick wall fell onto Swanston Street in Carlton.
Another woman, aged 19, suffered life-threatening injuries.
Mr Doyle says he would like to see tougher rules to force building owners to conduct regular structural checks.
"If there is one thing we can try to do, just from this awful tragedy, is to see if buildings around the city that are now getting older and sometimes you will find that parts of those buildings fall off. There is no power at the moment to require an owner to actually do a structural check of the integrity of the facade of their building."
