The ASTI say they would be willing to enter third party negotiations aimed at ending the teachers strike.
Around 500 secondary schools are closed as teachers take to picket lines around the country today.
Both teachers and the Department of Education are trying to blame each other for causing this strike which has affected 200,000 students today.
Minister Bruton said he is bewildered that teachers would strike over what amounts to one hour's work a week.
Teachers say that is not the issue, and that it is a matter of equal pay.
The two sides are far apart - but ASTI President Ed Byrne says they will continue talking if asked.
For now around 400 schools are set to remain closed tomorrow as teachers refuse to carry out supervision and substitution duties.