Mother Teresa Catholic Primary School principal Peter Hughes confirmed the new discovery on Friday morning, and said the school's architect was now going back through the original building specifications to track where the material might have come from.

Last week, just a few hundred metres away, material assessed as non-friable had been found in garden beds at the Harrison School.

Mr Hughes told The Canberra Times the asbestos discovered at Mother Teresa was mixed with crushed concrete gravel in a garden bed in the front car park.

He said the material had also been assessed as non-friable - meaning it is unable to be pulverised, crumbled or reduced to power by hand.

Both schools remain open, with garden beds in the Mother Teresa car park fenced off and every garden bed on Harrison School grounds also inaccessible.

In the case of the Harrison School, the ACT chief health officer Dr Paul Kelly has advised that the material should remain undisturbed and students and staff should not touch it.

But, based off assessments of the material as non-friable provided by the education directorate including reports of children playing in the garden beds, Dr Kelly considered the asbestos presented a low immediate risk.

"The chief health officer has recommended the material be remediated by a licensed asbestos removalist as a precaution," a spokesman told The Canberra Times on Friday.

At Mother Teresa, which had not yet been considered in Dr Kelly's assessment, Mr Hughes said he was trying to be open with parents. Children did not play in the garden beds where the material was found, which had since been fenced off, he said.

"It’s been found, [but] it's not overly dangerous at this stage, [and] a plan’s been going in place," he said.

"Kids have been advised to stay away from the area and there’s no other location where we have this crushed concrete on site."

On Monday, Mr Hughes asked the Catholic Education Office to test the car park's garden beds, after learning from the Harrison School principal that the asbestos at the neighbouring school was mixed with crushed concrete gravel and recycled building materials.

Testing was conducted at Mother Teresa on Tuesday and the results confirmed on Wednesday night before temporary fencing was put up and parents notified of the test results on Thursday.

Mr Hughes said it was unlikely that anyone would have had dangerous contact with the material given its location.

"Really, it would only be people coming through the car park that walked on it [who came into contact], but most of them use the pedestrian crossing," he said.

"I think we were just lucky to catch it, really."

He was unsure how the asbestos came to be at the school, which opened in 2010, saying he had only worked there for four years but the material would have been there since the school was built.

Mr Hughes said the asbestos assessor, John Robson, told him the asbestos at his school had likely come from the same place as the material found at Harrison School. Mr Robson declined to comment.

Catholic Education Office Canberra and Goulburn director Ross Fox said the asbestos would be removed from Mother Teresa outside school hours.

Asked how the asbestos came to be at the school and which contractor would have carried out the landscaping works in the car park, Mr Fox said he did not have that information.

"Our first priority is to make the place safe and the [area containing asbestos] has been fenced off," Mr Fox said.

"Then I guess we'll try and understand where it came from. Part of that will be whether it's related to the claims about asbestos at [Harrison School]."

A spokeswoman for the ACT government's education directorate said a search of department records had narrowed in on a list of contractors linked to landscaping at the Harrison School since its opening but investigators had not yet identified the source of the asbestos there.

Testing of the school's garden beds was now complete and final results were expected in the coming days.

"The advice from the licensed asbestos assessor is that the material remains non-friable despite being in the garden beds at the school," the spokeswoman said.

Principal Jason Holmes has been sending daily updates to parents since tests confirmed asbestos at the public school last Wednesday, and directorate officials have been on hand this week at drop-off and pick-up times to answer questions. But some parents who spoke to The Canberra Times said many remained unanswered, especially concerning students who played in the garden beds at the school.

The school and the directorate are remaining in close communication with Mother Teresa to share information, Mr Holmes said.

Michelle Young, a parent at Mother Teresa, said she was comfortable with how her own school was handling the situation.

"We got a letter home from the principal straight away letting us know that they'd found some asbestos and that it wasn't airborne," she said.

"It's not [a concern] and they're putting the right things in place."