The Human Rights Commission has demanded a guarantee that it has the opportunity to vet all Government legislation before formal publication.
Under the legislation setting up the commission, ministers can refer legislation to the commission where it may have "significant implications for the protection of human rights".
However, commission now wants the Government to agree a resolution that would "require" ministers to send new laws first to it.
The change, if made, would particularly affect the Departments of Health and Children, Education and Science, Social and Family Affairs. "For many departments it would not be greatly relevant, but it would for those ones," the commission president, Mr Maurice Manning, said last night.
"There may well be human rights issues. We would like to be involved at an early stage," said Mr Manning, who heads the body set up after the Belfast Agreement.
In a document lodged in the Oireachtas library yesterday, the Department of Justice said the Minister had intended raising the matter with Cabinet colleagues.
Meanwhile, the commission believes it should become accountable to the Oireachtas rather than to the Government to guarantee its independence.
Though established by law, the commission said links with the Departments of Justice, Equality and Law Reform and Finance "could fetter its autonomy and effectiveness".
The human rights body, headed by the former Fine Gael senator, is now in talks with the Oireachtas on the matter.
In a reply, the Minister for Justice, Mr McDowell, said it was "not easy to see" how making the commission accountable to the Oireachtas would increase "its independence or effectiveness".
If the commission cannot be made accountable to the Oireachtas, it should at least be linked with the Department of the Taoiseach rather than Justice, Mr Manning said. "Human rights abuses are committed by the State. Linking us to Justice creates the wrong perception," he told The Irish Times last night.
Acknowledging there was "some force" in the commission's argument, the Minister said, however, that this matter had been examined before the body was set up.
Mr McDowell had agreed that the commission's budget should be decided in future in direct talks between him and the body, rather than just with officials. But he rejected its demand for the establishment of an expert advisory group to "validate" the qualifications of future commission members.
In a reply, the Department of Justice said: "The Minister is of the view that given the commission's mandate and remit a broadly-based and balanced approach to the membership issues is absolutely essential.
"He has no difficulty with the idea of a selection committee, but at the same time he would not concede infallibility to such a body."
However, the Minister has indicated that he is prepared to consider a number of possible vetting models, including the one offered by the Judicial Appointments Advisory Board.
The commission has also sought full control over the number of staff it employs, the ranks at which they serve and the pay and allowances they enjoy.
These recommendations, said the Department of Justice, "ignore the central role and responsibilities of the Minister for Finance over Government expenditure".
Acknowledging that the commission had encountered staffing difficulties to date, the Department of Justice said there was a case for "putting more flexible arrangements" in place.