Minister for Education Jan O'Sullivan has said today's strike action by teachers "hasn't gotten us anywhere" and she is hoping that a further one-day stoppage will not go ahead.
She urged teachers to return to negotiations and to call off a second day of action planned for next month.
However, the General Secretary of the Association of Secondary Teachers, Pat King, said that, as it stands, a second day of strike action will take place in January.
Ms O'Sullivan said she was prepared to talk to teachers about resources but that negotiation needed to be a two-way process.
Second-level schools across the country were closed as teachers staged a one-day strike over Junior Cycle reform proposals.
Around 27,000 post-primary teachers engaged in the action, which resulted in a day off for around 350,000 students.
Speaking on RTÉ's Six One News, the minister said she hoped the unions would lift the veto on teachers assessing their students' work.
She said she had moved considerably from what was originally on the table after listening to their concerns.
Ms O'Sullivan said under the proposed reforms, the written exam would be worth 60% while teachers' assessment would be 40%.
She said the reforms would be introduced slowly with just one subject the first year.
Also speaking on RTÉ's Six One News, Mr King said there was time to avoid a second day of disruption and the ASTI was available to meet the minister.
Mr King had no doubt talks would take place with the minister but he said teachers wanted objective external assessment.
He said it was difficult to accept the pre-conditions that the minister had laid down. "We want to go in and talk about all the issues but the minister must listen," he said.
Mr King said the last place teachers wanted to be today was outside schools, however said they were defending education standards.
Thousands of teachers formed pickets outside their schools to give public expression to their opposition.
The industrial action was organised by the ASTI and the Teachers' Union of Ireland.
The executives of both unions are to meet next week and are expected to consider a date for a second day's strike in January.
ASTI President Philip Irwin said teachers saw the reforms as a "significant threat to education standards and education quality".
He said: "They are reluctantly taking strike action today in protest at what they see as a significant threat to education standards and education quality in Ireland.
"However, we are open to further engagement with the minister on this issue in an effort to seek a solution.
"We still believe it is possible to improve Junior Cycle education while maintaining the integrity of the education system."
Ms O'Sullivan said the strike could have been averted.
She said this morning that she was disappointed the unions did not come and have meaningful talks.
The reform attempt hit the rocks several weeks ago as talks broke down over the issue of teachers assessing their own students for Junior Cycle certification.
TUI president Gerry Quinn said: "Teachers fully recognise the importance of not relying exclusively on a terminal examination.
"Project, portfolio and practical work already form a significant part of many subjects, but, crucially, all elements are assessed externally.
"We are prepared to consider the extension of this practice provided it is done in a way which does not create more pressure on students."
Teachers in Lisdoonvarna striking today. Send your strike photos to @astiunion #juniorcyclestrike pic.twitter.com/XME0yUDtzp
— ASTI (@astiunion) December 2, 2014
Meanwhile, Minister for Public Expenditure and Reform Brendan Howlin said Ms O'Sullivan has moved a long way from the original plan.
Speaking on his way into Cabinet this morning, Mr Howlin said he would like to see movement with the reform agenda for students into the future.
Junior Cycle strike action - Drumshaughlin Community College, Co Meath #juniorcyclestrike pic.twitter.com/eo7uQ4gQqn
— Teachers' Union Ire. (@TUIunion) December 2, 2014
In Limerick, teachers on the picket lines said their objectivity will be open to compromise, particularly in smaller rural communities where they know parents and often socialise with them.
In addition, they say it puts many teachers in the same school in competition with each other, if some pupils are seen to do better than others.
They said with the current system pupils remain an anonymous number, and it does not matter where they live as they are marked anonymously according to effort.
