Some INTO members are calling for the union to hold an immediate ballot for industrial action.
The demand comes after the union was forced to deny reports yesterday that it had accepted the new public service pay deal.
The INTO said it has simply agreed to participate in a review of pay equality - but internal activist group Glór says entering into these talks is a de facto acceptance of the deal.
Group spokesman Gregor Kerr said the union is ignoring its members.
"Eighty-nine percent of the members of the union have given the leadership a mandate that said: 'We want pay equalisation now and we're not content with a review'," he said.
"And we believe what should have happened is that the INTO leadership should have taken a ballot for industrial action and strengthened their hand in any negotiations that would take place with the Government.
"And negotiations and talks have to take place outside of the context of the Public Service Stability Agreement."