The Children's Right Alliance is calling for pupils to have the choice of sitting the Leaving Cert or accepting predictive grades.
Officials are now considering scrapping the exams, which are due to take place on July 29.
A meeting is taking place today between stakeholders and the Department of Education, but no decision is expected this week.
Tanya Ward, chief executive of the Children's Rights Alliance, says clarity is needed and that the situation is "very unfortunate."
She says: "I think the uncertainty is very unfortunate because we know from young people themselves that they are finding the stress of not knowing whether the Leaving Cert is going to progress is causing huge burdens on them.
"I think they need to give young people an option to either sit the Leaving Cert or proceed through predictive grading.
"Because some young people are likely to benefit from doing the exam and other young people are likely to benefit from predictive grading."
Meanwhile, the normal timetable for the Leaving Cert exams will not operate this year, the Association of Secondary Teachers in Ireland (ASTI) has told its members.
With the schedule for the 2020 written exams to be confirmed at the beginning of June, the standard arrangements for the written exams will not be in place this year, according to the union.