Surveys have shown that most S5 students will start studying for new Highers next term, although the situation varies across Scotland.
In some areas, individual schools have been allowed to take decisions over whether to delay the new Highers, while other councils have taken a decision that covers all schools.
The Educational Institute of Scotland (EIS) teaching union said it was right that councils had been prepared to let schools decide whether the new Highers should be delayed.
Education convener Susan Quinn said: "The EIS heard concern from teachers regarding the introduction of the new Highers, as schools were still working flat-out on the delivery of the new National 4 and National 5 courses.
"While the Scottish Government ruled out the call for a [blanket] one-year delay, the EIS did welcome the decision to allow individual school departments to opt out of the new Highers if they felt this was in the best interest of pupils."
A Scottish Government spokeswoman added: "What is most important is that each school and their authority work with parents and pupils to make use of the flexibility in the way which best serves the interests of the pupils."