A European students' body has urged the Minister for Education, Mr Dempsey, to rule out the re-introduction of third-level fees for those who can afford them.
As student protests took place in Athlone and Carlow, the European body for students, the National Unions of Students in Europe, said it condemned Mr Dempsey for considering the idea as part of a review.
The group said it would instruct its members in European states to protest if Mr Dempsey visited local colleges.
The group said it would "assist the Union of Students in Ireland in its continuing campaign for free education for all and the union's work in developing a student support system which would allow socio-economically disadvantaged students access to higher education".
The protest in Carlow attracted about 2,000 students, while about 1,000 gathered in Carlow.
The president of USI, Mr Colm Jordan, said students were going to keep the pressure on the Minister until he unequivocally ruled out re-introducing fees.
Mr Jordan said: "USI sincerely hopes the Government does not interpret the result of the Nice referendum as being an endorsement.
"As Minister for Education, Noel Dempsey has a duty to increase the numbers of disadvantaged students taking part in third-level education.
" So far his actions could only be interpreted as doing the opposite."
He said the Europe-wide student union group represented about 10 million students across the continent and USI was glad to get their backing.
"Despite rising costs of living in every town and city in Ireland, the grant was increased on a scale of just 70 cents for the lowest grant rate and €3.50 for the highest.
"Our ongoing campaign railing against this deceit is growing stronger with every march and demonstration.
"Along with the powerful European endorsement, we will be meeting with members of the UK's national students' union, the NUS, on December 9th seeking support for our campaign," added Mr Jordan.
Mr J.P. McArdle, president of the student's union at the Institute of Technology in Carlow said students were sending a message to local Fianna Fáil TDs Liam Aylward and M.J. Nolan that students would not allow the Government to threaten their right to a free education.