Liberton High in Edinburgh remains shut after the death of the schoolgirl, named locally as Keane Wallis-Bennett.
A church vigil will be held later today, when classmates will be given the opportunity to light candles for the first year student.
Speaking in the Commons, Prime Minister David Cameron described the accident as "absolutely shocking" and said lessons should be learnt to prevent any future tragedies.
Police and the Health and Safety Executive (HSE) are leading the investigation into the pupil's death and a programme of building checks by surveyors is under way at the school, in the south of Edinburgh.
The city council was recently fined £8,000 after a Liberton pupil was injured falling down a lift shaft at the school in December 2011.
Scottish Justice Secretary Kenny MacAskill, MSP for the Edinburgh Eastern area, said the school "has its challenges" but he did not believe there were problems with health and safety.
He told BBC Radio Scotland's Good Morning Scotland programme: "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 the girl's death was a double blow for the school after the death of pupil Jamie Skinner, 13, who collapsed while playing football for Tyncastle FC at the end of last year.
Mr MacAskill said: "The school will bounce back, it's had its challenges. This is a tragedy but it remains part of the bedrock of that community."
Asked if there were concerns about health and safety at Liberton High, he 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."
Edinburgh City Council said a survey of all its schools was carried out between 2012 and 2013 and no concerns were identified with the free-standing wall at Liberton High.
The school will not reopen this week and a full survey will be completed before pupils return from the Easter holidays in three weeks.
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 tragedy was raised at Prime Minister's Questions in the House of Commons by Edinburgh South MP Ian Murray, whose constituency includes the Liberton school.
He said: "I'm sure the Prime Minister and the whole House would wish to send their condolences to the headteacher Stephen Kelly, the staff, teachers and pupils at the school, her friends and of course her family, who sent her to school yesterday morning, for her never to return home."
Mr Cameron replied: "This was an absolutely shocking accident that people will have seen across the country, and their hearts will go out to the family and all those involved in the school.
"Clearly the lessons will have to be learnt to make sure that accidents like this can't happen again."
Liberton Northfield church will be open this afternoon and evening for pupils and members of the local community who would like to sign a book of condolence and light candles.
Liberton chaplain Reverend Cammy Mackenzie said: "We recognise the impact this is having on the community and we will be there for anyone who needs us. The church will remain open for as many days as it is required."