Liberton High School has had “difficulties with fragmenting and fraying to the fabric” of the building, according to Justice Secretary Kenny MacAskill
But he said he did not believe there were problems with health and safety at the school.
Mr MacAskill, the MSP for the Edinburgh Eastern area, told BBC Radio Scotland’s Good Morning Scotland programme of his “shock and disbelief” at the death.
“It’s hard to imagine the situation of a child going off to school on a spring day never to return, and our hearts and thoughts go out to the family and the wider community and pupils,” he said.
Mr MacAskill welcomed work by the city council to check similar walls, saying this would “reassure pupils and parents”.
He said the girl’s death was a “double blow” for the school after the death of fellow pupil Jamie Skinner, 13, who collapsed while playing football for Tyncastle FC at the end of last year.
Mr MacAskill said: “It is a devastating blow, the loss of a pupil there, because of the tragedy that affected them on the football field. It’s a double blow for a community that’s quite tight knit.
“The school will bounce back, it’s had it’s challenges. This is a tragedy but it remains part of the bedrock of that community.”
Yesterday’s incident came weeks after the council was fined £8,000 after a girl at the school was seriously injured when she fell more than 16ft down a broken-down lift shaft.
The schoolgirl, then aged 15, suffered three fractured vertebrae and a sprained wrist as a result of the fall in December 2011.
Asked if there were concerns about health and safety at Liberton High, Mr MacAskill said: “I don’t believe so. The school, as with many schools of that era, the late 50s early 60s, has its challenges. There was storm damage a few years back that caused considerable difficulties and the incident for which the council was fined.
“But notwithstanding the difficulties with fragmenting and fraying to the fabric, it’s a good school in which the head and past head have done a remarkable job in making it a very good school for the local community.”
He stressed the council had been doing a “good job” on school maintenance, despite financial pressures.
“There are budgetary pressures for all aspects of government, national and local, but I think the council are doing a good job,” he said.
“They are working their way through the school estate, many schools are being replaced.
“I recognise that the city council has always put the safety of pupils as paramount, that’s why I welcome the review to ensure the situation is safe in every school. They do have to prioritise but I do believe they have been doing a good job.
“Everything that needs to be done immediately is being done and we need to allow the statutory agencies to carry out their investigation.
“If there are lessons to be learned I would expect them to be implemented, whether by the local council, other local authorities or indeed by my colleagues and myself in national government.”
The council said a survey of all its schools was carried out between 2012 and 2013 and no concerns were identified with the wall at Liberton High.
A spokesman said: “As a precaution, specialist council building services staff will be surveying all similar walls in schools where we know that they exist. The survey work will begin early on April 2.
“As a further precaution, a full survey will be carried out on Liberton High School in the coming days before the main school building reopens to pupils.”
First Minister Alex Salmond visited the school in December and has already pledged a “rigorous investigation” into the incident.