ASTI members in Thurles called for the planned three-day stoppage next week to be abandoned in an attempt to draw the Government into talks.
Teachers at the Presentation Secondary School, Thurles, in a letter to their standing committee, highlighted the impact of the ASTI industrial action on students and called for the strike to be called off next week.
ASTI general secretary Mr Charlie Lennon said the union's standing committee would examine the views expressed in the letter.
"They have had a lot of correspondence from different branches and members saying different things. They will look at the bigger picture, the implications and where the current position is at.
"There are different views from members. Some are for an all-out strike, there are people who would like to make it more intensive and others who would make it less," said Mr Lennon.
"There has to be some kind of initiative to try to get the parties to get together to find a solution," Mr Lennon added.
Mr Noel Buckley, chairperson of the ASTI Tipperary branch, confirmed the "contents of the letter were about the serious impact the industrial action is having on students.
"It asks the standing committee to suspend industrial action next week in the hope the Taoiseach will talk to us. They hope that if we drop the three days of industrial action next week that the Government will talk to us," said Mr Buckley.
"It is no harm to have different ideas floating around but it is a little naive to think that by dropping the industrial action Bertie Ahern and Michael Woods will come to talk to us," added Mr Buckley.
Ms Mary Anne Fogarty, a shop steward for the ASTI at the Thurles school, said her members were not "taking away from the union in any way".
"We are fully supportive of the union, but we would very much like to be back in the classroom," said Ms Fogarty.
"We are not, in any way, a breakaway group," added Ms Fogarty, who said the letter was an internal memo within the ASTI and was only a "suggestion to the standing committee to get talks going".
The call to end the strike is understood to be aimed at helping alleviate pressure on exam students and as a gesture to the Government to bring it into negotiations.