Sinn Féin and a number of anti-EU groups indicated yesterday that they will reject the EU constitutional treaty.
But the Greens,who opposed both Nice Treaty referendums, said the party membership would decide whether to support or reject the constitution.
The general secretary of Sinn Féin, Mr Robbie Smyth, said the treaty had not addressed the party's concerns about the loss of sovereignty and the emphasis on the rights of business over the rights of individuals.
"We had very deep concerns about aspects of the draft treaty and it seems at a first reading that those concerns - about the whole privatisation agenda and the EU military aspect for example - haven't been addressed," said Mr Smyth.
While the Sinn Féin ardchomhairle had not yet discussed the treaty in detail, Mr Smyth said the party was likely to oppose it on the basis that its concerns about the draft produced by the European Convention were not resolved in the final document.
The Green Party's foreign affairs spokesman, Mr John Gormley, could not say whether the party would support the treaty in advance of a vote by the membership at a special seminar.
"I can only report back after the seminar has been held. It would be wrong of me to pre-empt what those discussions would conclude," he said.
Asked whether the party leadership would urge members to back or reject the treaty, he said: "We've said very clearly that we're not going to impose anything on the membership."
However, it is known that the Greens have a particular problem with the retention in the treaty of the Euratom agreement, which allows governments to fund nuclear plants such as Sellafield without reference to EU rules on state aid. The Greens had sought a sunset clause which would have rendered the Euratom null and void after a period.
The chairman of the pro-neutrality Peace and Neutrality Alliance, Mr Roger Cole, said it was "virtually impossible" for the group to advocate support for the treaty if it did not contain a protocol excluding Ireland from the EU Rapid Reaction Force.
Mr Cole said the group will seek legal advice to ascertain whether such a protocol could be added to a constitution. Such a protocol should exclude Ireland from funding and taking part in the Rapid Reaction Force.
The European Alliance of EU-critical Movements said the treaty would override national laws and national constitutions if it were enforced.
The co-ordinator of the alliance, Mr John Boyd, said the constitution would bring about "a huge transfer of powers" from member-states to EU institutions and from small to big countries.
"With this constitution the EU is continuing on its present path, at an increasing pace, to a highly centralised EU state with global ambitions," Mr Boyd said in a statement circulated in Ireland by the anti-EU campaigner, Mr Anthony Coughlan.
