Minister for Children and Youth Affairs Charlie Flanagan has said a high-level interdepartmental review on the mother-and-baby homes has been submitted to Cabinet.
He said the next stage was for the Government to make recommendations on the terms.
The minister said he was deeply aware of the pain suffered by individuals affected and wanted to deal with it in a sensitive and timely manner.
His intention is to bring recommendations before the House before the recess to make an order to establish the commission.
He was responding to a question from Fianna Fáil TD Robert Troy. He said there was wide cross-party consensus and thanked Mr Troy and members of the Opposition for their approach.
The minister said 25,000 files had been established from the Sacred Heart Adoption Society and these will form part of the investigation.
He told Sinn Féin's Caoimhghín Ó Caoláin that he would report back before 17 July.
Mr Ó Caoláin asked if all survivors and victims of these homes would be included.
Minster Flanagan said they wanted to establish the truth and historical context of the issue, taking into accounts the needs of children of today.
Earlier, Taoiseach Enda Kenny said the Cabinet briefing was likely to be only the beginning of a long process.
Speaking to reporters this morning, Mr Kenny said this was a story that had gone on for years.
The Irish Human Rights and Equality Commission Designate is calling for the Commission of Investigation into the homes to be broadened in scope, to comply with the State's human rights and equality obligations, and offer effective remedies and redress.
Betty Purcell, Acting Chair of the Irish Human Rights and Equality Commission, said "the operation and oversight of institutions such as mother-and-baby homes and Magdalene Laundries raise very serious questions about the extent to which the State has complied with its human rights obligations under the Constitution and under international human rights law."
She said it was essential that the State ensured that a human rights and equality framework be applied so the terms of reference, the process of the investigation and redress of alleged historic human rights abuses are informed by and fully compliant with the State's human rights obligations.
Ms Purcell said that the Commission of Investigation Act 2004 may need to be amended to allow this.
She said the investigation must be "independent, impartial, transparent, adequate and effective, and timely".
It must have powers of compellability based in statute and be able to source all information and documentation to establish and properly test allegations of human rights abuses, she said.
Ms Purcell also said victims should be allowed, at their request, to give evidence in public.
The IHREC Designate today published its submission to Minister Flanagan on the proposed Commission of Investigation.