The INTO is to investigate the possibility of accommodating the Minister for Education, Mr Dempsey's request for a Your Education System (YES)-style forum at its annual conference.
In a surprise move, it says it will also be seeking talks with the Department of Education and Science to see if an agreement can be reached with Mr Dempsey over his attendance at the conference.
Such an approach differs greatly from that adopted by other teaching unions, and will be seen by some as a significant concession to Mr Dempsey.
According to Mr John Carr, the general secretary of the INTO, the INTO believes its annual congress is a mechanism for "doing business" on educational and industrial relations issues. Mr Dempsey's attendance at the congress was an important part of that.
"Teachers want to hear from the Minister for Education and Science of the day," he said. "Clearly the Minister has expressed a preference for doing business through the format of a YES meeting. This could be accommodated.
"The INTO takes the view that it is important that the Minister engages with teachers, and details priorities and policies through an address to congress."
The INTO says it wants to see if both Mr Dempsey's request for a YES meeting and the traditional ministerial address to the conference can be facilitated.
While it is understood the holding of a YES meeting does not depend upon Mr Dempsey addressing the conference, it is believed the hope is that he would be willing to do both.
The INTO has also agreed to consider the possibility that such a meeting might take place later, outside congress, if required.
Last month, it was revealed that Mr Dempsey had written to all three teaching unions saying he wanted to abandon the traditional practice of attending the conferences.
Instead he wanted to hold a YES-style forum on the future of education at each of the conferences.
However, a response to the Minister from the ASTI revealed that it was unwilling to consider any changes to the current format of its conference.
In a letter to Mr Dempsey, Mr John White, acting general secretary of the union, expressed his hope that Mr Dempsey might accept the invitation to address its conference.
He also stressed that the annual conference of the ASTI was the "supreme governing body of the association".
He said given that its structure and programme was organised by a democratically-elected committee, it would not be possible to depart from the current format.
A spokeswoman for Mr Dempsey last night said that the Minister was currently in Japan on official St Patrick's Day business.
However, he would be awaiting an official response from the INTO before commenting further.
Mr Carr will be writing to Mr Dempsey today to seek a meeting with the Minister this week.