The Transport Minister said that teachers will have to face legislated pay cuts, if they do not accept the Haddington Road Agreement.
The TUI and the ASTI have both indicated they will reject the latest agreement, because they say it is too similar to the Croke Park II deal.
Legislation will be brought before the Dáil next week, which will give effect to public sector pay cuts and a freeze on increments.
Transport Minister Leo Varadkar said the teachers will face those cuts, if they do not sign up to the revised pay agreement.
"The legislation will pass through the Dáil next week so the choice is between the Haddington Road Agreement and the pay cuts that are being imposed by government," he said.
"It's really up to secondary teachers themselves, strike if they want to but those changes will come in on the 1st of July."