Almost 500 children at Flora Stevenson Primary School were evacuated to nearby Broughton High School shortly after 11am for health and safety reasons.
But the city council confirmed the asbestos had actually been exposed during work undertaken while the school was closed.
It is understood the problem may have been raised after an inspection in the morning.
The council said subsequent inspections had found the building to be safe, but further tests would take place today, with the school set to reopen on Monday.
Parents today said they were “horrified” by the possibility their children might have been exposed to the substance.
They were informed by text message and e-mail shortly after 11am that due to “a health and safety issue”, pupils had been transferred “on a precautionary basis”. Mum-of-three Annabel Ross, whose six-year-old daughter Lucia is a primary two pupil at the school – but was off sick yesterday – said she was “appalled” that the pupils were allowed to enter the school after asbestos had been disturbed.
The 36-year-old, who lives in Craigleith and volunteers as a classroom assistant at the school, said: “If the asbestos was disturbed out of school hours, I’m shocked, horrified and appalled that they proceeded to open in the morning.
“I think that is a blatant disregard for the safety of children and staff. The trouble with asbestos is you only need to breathe in one particle for it to cause problems later on.”
Ms Ross claimed asbestos had been a problem at the school before. She added: “Before they started putting an extension on a few years ago, they had to remove the old music school building, which had asbestos in the roof.”
Another concerned parent, Mandi Dick-Fairley, 46, said the asbestos could have affected the health of her son, who has seasonal asthma. She said: “I got a text message at about 11.20am, so the pupils would have already been in Flora Stevenson for two-and-a-half hours, which concerns me.”
It is understood that the asbestos was disturbed while workers were installing a door.
Labour’s education spokesman, Paul Godzik, said: “It’s a very concerning situation. I will certainly be asking the director of education for a full report.”
Chair of Stockbridge and Inverleith Community Council, Nigel Bagshaw, whose ten-year-old son Matt is a pupil at the school, added: “Perhaps the council should have an audit of all the schools to make sure there is none in any others.”
The city’s head of schools, Mike Rosendale, said: “A small quantity of asbestos has been disturbed during routine work which took place out of school hours.
“An independent inspection was carried out yesterday afternoon and has indicated the building is safe.”