The Department of Education has said it is still planning to bring Leaving Cert students back to class for two weeks before the exams start.
That is despite the Government confirming schools and colleges will not re-open until September.
The department is still planning for the Leaving Cert to go ahead on July 29, with the possibility of classes two weeks beforehand if social distancing can be observed.
However, Fianna Fáil want the Leaving Cert to be cancelled and college capacity expanded on a once-off basis.
The party's education spokesperson Thomas Byrne said there is still no certainty for sixth year students.
Deputy Byrne believes the exams are causing too much stress.
He said: “Under this roadmap primary and secondary schools are not set to open until autumn, yet in an announcement made by the Education Minister a few weeks ago, the Leaving Cert was earmarked to begin at the end of July.
Leaving Certs are essentially back where they started in March – unsure what the situation is, and whether the exams will be going ahead.
“While this is a challenging time for everyone right now, it’s unfair to underestimate the stress and anxiety that Leaving Cert students are feeling as the uncertainty about their exams and their futures continues. The inequities inherent in self learning online are well known."
He called on the Government to stop what he described as "wait and see approach" with the Leaving Cert.
He said: "It is becoming clearer with every week that passes that it is simply not tenable for it to proceed. The time has come to make the call to cancel the Leaving Cert and take the pressure off students, parents and their teachers.
“I've discussed alternatives with some universities and with Minister McHugh over last few weeks. They do exist and we must now switch our focus to them.
"The current situation is unacceptable and unfair and is causing untold psychological damage to these students”.