Update: Sinn Féin's education spokesperson Donnchadh O'Laoghaire has said the health of students and staff needs to be put first in any decision to reopen schools.
It comes as the Health Minister suggested schools may be able to reopen one day a week before the summer break.
Donnchadh O'Laoghaire believes schools should only reopen if its in line with medical advice:
He said: "In my view, the priority has to be the safeguarding of public health and the advice of the National Public Health Emergency Team needs to be followed when it comes to decisions around mass gatherings of any kind or reopening of businesses or schools, for that matter."
Mr O'Laoghaire went on to say that the Leaving Cert is a tough experience even before a pandemic is factored in as he called for a dedicated helpline for Leaving Cert students.
The party said the mental health and well-being of current sixth years must be made a priority.
Mr O'Laoghaire said: "The thing that comes across is that they are feeling serious pressure, they are feeling serious anxiety, and the lack of clarity around the Leaving Cert has contributed massively to that.
"The Leaving Cert is a difficult experience in any year, it is an incredibly difficult experience to try and do that with the background of a global pandemic affecting everyone."
In the meantime, the Teachers Union of Ireland has told its members there is no guarantee the rescheduled Leaving Cert can take place.
In a document released to secondary teachers it says public health advice will dictate whether the state exams can be held in late July or early August.
It says the tests taking place relies on a decision made in June, when the State Exams Commission is due to release a proposed timetable.
The Government is considering reopening schools for one day a week as part of plans to ease the Covid-19 restrictions.
The Health Minister's told the Sunday Independent it is one of the options being looked at.
He also says pubs packed with people won't be allowed until there's an effective vaccine.
Minister Harris has also thrown into question large gatherings like GAA matches or festivals such as Electric Picnic.
"We're going to have to very shortly make a decision on these mass gatherings," he said.
"I think it's unlikely that we're going to see mass gatherings come back any time soon. I think we're going to have to keep up our social distancing, even if we can lessen some of the restrictions in place."