The country's schools could be closed until May, Taoiseach Leo Varadkar has told his Fine Gael colleagues - hours after the Education Minister announced the Leaving Cert and Junior Cycle orals and practical exams are being cancelled.
Minister Joe McHugh has yet to make a decision about the written exams in June.
During a teleconference call with his parliamentary party, Mr Varadkar said he expected school closures to extend beyond March 29.
In a statement last night, Fine Gael parliamentary party chairman Martin Heydon said the Taoiseach told TDs: "The restrictions on schools opening could be extended into April or May.
"The Fine Gael president said there will be big increases in positive cases over coming days with increased testing taking place across the country.
"He said all of Government was pulling together on fighting the virus. He said the benefits of social distancing may not be seen for five to 10 days."
It came as principals and teaching unions welcomed the cancellation of Leaving Cert and Junior Cycle oral and practical exams.
Candidates will be awarded full marks for these elements of their exams - worth between 20pc and 50pc of the total marks - with Education Minister Mr McHugh describing it as the fairest approach in the circumstances. It means that students cannot be awarded a lower mark than they would have achieved in the test, although candidates not sitting those subjects may feel at a disadvantage.
There was significant support for the move, with National Association of Principals and Deputy Principals (NAPD) director Clive Byrne saying the announcement would come as a relief to students.
The Teachers' Union of Ireland (TUI) said that, while any approach would have its drawbacks, the announcement provided students with much-needed clarity.
The Association of Secondary Teachers Ireland (Asti) said it would allay students' anxiety around the uncertainty over the orals' and practicals' timing.
The cancelled exams were scheduled to take place over two weeks, starting next Monday, but could not get under way because of the nationwide closure of schools.
The shutdown will be reviewed next week, and the closure is fixed only until March 30, but the earliest possible return is likely to be after Easter, and only then if circumstances allow. Yesterday's announcement affects oral tests in Leaving Cert Irish, French, German, Spanish, Italian, Russian and Japanese, practical performance tests in Leaving Cert Music and Junior Cycle Music and Home Economics.
Other exam-related measures announced by Mr McHugh included an extension of deadlines for students to complete project work and coursework in a number of subjects to May 15.
But there is no change in the schedule for a second phase of practical exams between April 27 and May 8; for the final written exam in the Leaving Cert Vocational Programme (LCVP); for a range of oral and practical tests in the Leaving Certificate Applied (LCA) programme; or for the first exam in Leaving Cert Computer Science, on May 27.
The big focus is on what happens with the written exams in June and Mr McHugh said education chiefs were still working on the basis that they would go ahead, although there were "a lot of unknowns, a lot of assumptions about next week, never mind May or June".
He said the Department of Education would continue to work with the State Examinations Commission to monitor the Covid-19 situation in terms of its potential impact on the other later scheduled components of the State exams.
"We will continue to respond at the right time and in the right way, with the impact on our students at the forefront of our minds," he added.
Mr McHugh said the Government was hugely grateful for the effort, commitment and energy that students and teachers were putting in to continue education in difficult circumstances, adding: "I urge you all to keep up the momentum and focus on preparing for the exams."
NAPD director Mr Byrne said the current group of sixth years would not be disadvantaged and that the exam system would "do everything to enable them to proceed to the world of work, further education or higher education."
Some 126,000 students are due to take the State exams, with 65,190 entered for the Junior Cycle exams and 61,053 students scheduled to sit the Leaving Cert.