The Minister for Education, Dr Woods, has been asked to waive this year's Leaving and Junior Certificate examination fees as a way to compensate students for the loss of teaching time during the secondary teachers' dispute.
The National Youth Council of Ireland (NYCI) said the fees should be dropped because students had lost significant classroom time and suffered serious stress during the dispute.
It held a protest outside the Department of Education Dublin yesterday to highlight the issue.
The Association of Secondary Teachers, Ireland (ASTI) has been taking strike action since mid-November.
Most students have lost 10 days already and if the current talks fail, further industrial action up to April is planned.
The Department normally charges Leaving Cert students £55 and Junior Cert students £52 to sit the exams.
The NYCI president, Mr James Doorley, said Dr Woods could make a "significant gesture" by dropping these charges.
He said another reason to do this was because the exams might not take place this year and if they did it would be under unusual and disruptive circumstances.
"As it stands the teachers are likely to get back the pay that was deducted as a result of their action, the Government will get industrial peace, but the students will get nothing," Mr Doorley said.
"Throughout this dispute all sides have mentioned their concerns about the impact of the dispute on young people.
"There is now a meaningful opportunity for the Government to put those sentiments into a direct and beneficial action."
A spokesman for the Minister said a letter about the issue from Mr Doorley would be brought to his attention.
Dr Woods was not in the Department yesterday and was visiting third-level colleges in Cork.
Students have to pay the fees within the next fortnight. Some pay by bank giro while in other cases the school collects the money and passes it on to the Department.
School principals have said pupils will not lose out because of the strike, but some schools have given extra lessons to ensure this does not happen.
No progress was reported in the ASTI talks at the Labour Relations Commission (LRC). The union and Government representatives spent several hours discussing various proposals, but they were understood to be far from reaching a final agreement.
The talks are being overseen by Mr Tom Pomphrett of the Labour Relations Commission.