The Cabinet will discuss the bill to hold a referendum on the Eighth Amendment at its meeting tomorrow morning.
Ministers will also discuss a policy paper that will outline the Government's approach to the legislation it will introduce if the referendum is passed.
Approval will be sought on the wording of the question to be put to voters in the referendum, which is expected to be held in late May.
The Eighth Amendment recognises the equal right to life of the mother and the unborn child.
Voters are expected to be asked whether or not they want to repeal the Eighth Amendment. They will also be asked to replace it with new wording to be put into the Constitution.
There are unlikely to be changes to the draft wording already agreed, which states "provision may be made by law for the regulation of termination of pregnancy".
However, this is subject to further consideration by both the Attorney General and Cabinet.
It is expected that the policy paper will be strongly in line with the recommendations of the Oireachtas committee that looked at the issue.
One of its key findings is to allow terminations with no restriction up to 12 weeks.
The policy document is expected to be in line with this proposal, but the words no restriction or without restriction will be replaced by "without specific indication".
It is also expected to propose that a woman would be initially assessed by a medical practitioner and a time period would be required to elapse between the initial assessment by a medical practitioner and a termination being carried out. It is not clear if it will state how long that time period will be.
In relation to terminations of the grounds of health, there will be no distinction between a risk to the physical or mental health of a woman.
Two medical practitioners will be required to assess a termination on the grounds of a risk to the health of a pregnant woman or in cases likely to lead to potential fatal foetal abnormalities.
In line with the Oireachtas committee's recommendation, it is proposed that there will be no gestational limit in cases of potential fatal foetal abnormalities.
The policy document is due to be published tomorrow or on Friday and is not a draft bill. That will be published at the end of the month.
However, it has become clear the proposed legislation that the Government intends to introduce if the referendum passes will become a significant issue in the referendum campaign.
Earlier, the Taoiseach agreed to give the Attorney General "the remains of the day" to study the judgment by the Supreme Court.
Speaking in the Dáil, Leo Varadkar said the Cabinet would meet tomorrow at 11am to hear the Attorney General's advice.
Minister for Health Simon Harris said he was considering today's ruling and awaiting the advice of the Attorney General.
He said: "This bill will contain the wording to be put to the people in a referendum at the end of May. I look forward to the people having their say on this very important issue."
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This morning, Chief Justice Frank Clarke said in delivering the ruling that the unborn's constitutional rights are confined to those in the Eighth Amendment.
The judgment was unanimous with all seven judges agreeing in the landmark case about the extent of the rights of the unborn.
The State appealed a High Court finding that the unborn has constitutional rights beyond the right to life in the Eighth Amendment.
This was an immigration case involving a Nigerian man, his Irish partner and their child who was just over three weeks away from birth when the proceedings began.
The man wanted the Minister for Justice to revoke a deportation order made against him. The High Court found his unborn child had rights under the Constitution beyond the right to life.
Justice Department to analyse ruling
Minister for Justice and Equality Charlie Flanagan said his department will analyse the ruling "in relation to the implications for the status of potential deportees from the State with regard to their family status".
Fine Gael Senator Catherine Noone, who chaired the Oireachtas Committee on the Eighth Amendment, urged all to accept the court's judgment "in good faith" and "move forward in a civilised and respectful manner, as has been the case for the most part so far".
Labour's Jan O'Sullivan said the decision "paves the way for the Oireachtas to debate with clarity the wording of the proposed Government referendum".
The National Women's Council of Ireland, Coalition to Repeal the Eighth Amendment, and Abortion Rights Campaign also "welcomed the certainty and clarity provided by the Supreme Court ruling on the rights of the unborn".
The country's Catholic bishops have reiterated that the right to life of the unborn is not conferred by the Constitution.
They said that it would be a shocking step if society declared that any category of human being should be deprived of that right.
The Pro Life Campaign said the Supreme Court ruling that no constitutional protection for the unborn exists outside of Article 40.3.3 "shows the importance of keeping this life-saving provision in the Constitution".
The campaign's legal adviser, Professor William Binchy, said: "The court has made it clear that unborn babies, up to birth, would have no constitutional protection against the legislation that the Government intends to introduce."
The Iona Institute said the ruling "makes the forthcoming referendum more important than ever".
Spokesperson Maria Steen said: "The Irish people have now become, in effect, the last line of defence in Ireland for the unborn child."
The Save the 8th group said the ruling "confirms that if the Eighth Amendment is abolished, then the only constitutional protections enjoyed by unborn children would be abolished along with it".
Referendum bill may be discussed in Dáil tomorrow or Friday
In the Dáil, Mr Vardakar, responding to a question from the Sinn Féin Leader Mary Lou McDonald, said there is a possibility of the referendum bill being discussed in the Dáil tomorrow night or on Friday.
The publication of the bill will allow for the formal establishment of a Referendum Commission to begin work almost immediately.
The Taoiseach said the debate will be profoundly "deep and difficult" for a lot of people in Ireland and he expressed his "strong wish" that it be respectful and never personalised.
"People are entitled to their personal opinions on this deep issue of conscious," he said.
"Above all, the referendum will be about asking the public about changing our Constitution and our basic and most fundamental law to say we as a country, we as a people, we as a State, trust women to make these decisions for themselves."