The pay claim from second-level teachers can only be dealt with inside the terms of the national pay deal, the Programme for Prosperity and Fairness (PPF), the Taoiseach warned yesterday.
Mr Ahern said he was disappointed the strike was going ahead, but he was not interested in starting a war with secondary school teachers.
"The Government has no interest in starting a war with anyone, least of all these children's teachers, " he said.
Asked if the Government would consider giving into the ASTI claim, he replied: "We cannot do this in isolation from a programme that is not yet a year in existence. The Government can't have a two-tier system. I think everybody knows that".
Mr Ahern was speaking on RTE Radio 1.
He also stressed that the PPF had been extensively negotiated and debated in Government and with the Irish Congress of Trade Unions.
"I hope to quickly get back to a resolution of the issues within the PPF," he said.
A spokesman for the Minister for Education, Dr Woods, said he still hoped the ASTI could resolve the dispute within the PPF.
"The Minister's door remains open to them if they want to have discussions," he said.
The National Youth Council of Ireland said students were being caught in the middle of the pay dispute.
It said removing eight days from a nine-month academic year would "take a serious toll" on exam preparations.
"Students have enough to deal with in preparing for exams without having to deal with industrial action by teachers. Whatever about the rights and wrongs of the teachers' pay claim for more money and the Government's response, students will be caught in the middle," said Mr James Doorley, president of the council.
"Although a large number of students will be happy to have a few days off, a huge number will be worried about the possible effects on exam preparations and will not welcome the disruption," he added.
"Young people's education should not become a casualty of this dispute.
"We would urge both parties to use the industrial relations machinery available to them to resolve this dispute."
Teachers United, a group of teachers opposed to the national pay deal, said members of the other teacher unions - the Irish National Teachers' Organisation (INTO) and the Teachers' Union of Ireland (TUI) - should visit ASTI pickets today and show solidarity.
"Our union leaders are trying to dampen the growing militancy and support for ASTI among rank-and-file members of the INTO and the TUI," said a statement.
"It is estimated that after 15 years in the job, teachers are being paid £10,000 less than other graduates. As a result more than half the secondary schools in Ireland had major difficulties recruiting teachers this year," it added.