Taoiseach Leo Varadkar said the Dáil will sit longer into the summer to facilitate the passage of new legislation on abortion.
He said he agreed with the suggestion of Fianna Fáil leader Micheál Martin that the Dáil be extended into the summer recess "to allow this matter along to be legislated for, and to get to second stage before the summer recess".
But he said it would be the end of the year or 1 January 2019 before the Government could give full effect to the legislation.
However, the Taoiseach said a lot of work had been done around the general scheme of the bill.
Mr Varadkar was responding to the Solidarity/People Before Profit TD Ruth Coppinger on promised legislation.
She asked if the legislation had been written or prepared and stressed that women who took abortion pills today must not be penalised or criminalised.
Ms Coppinger also expressed hope that the cost of abortions being €300 was just a rumour.
The Taoiseach said it would be treated as normal healthcare and the same rules as the General Medical Card Scheme would apply.
He also said that his initial impression was that women who were resident in Northern Ireland would be able to travel south of the border to avail of abortion services.
Taoiseach believes women who live in Northern Ireland will be able to access abortion services south of the border pic.twitter.com/Rf8UNg5Iht— RTÉ News (@rtenews) May 29, 2018
This afternoon, Mr Varadkar said the speed of the legislation passing would only be tempered by a determination to get it right, and to ensure no flaws open it up to legal challenge and delay.
He also noted that the Government would introduce sex education and a wider availability of contraception to ensure abortions were rare.
Earlier, Minister for Health Simon Harris said it was important some realism was injected into the discussions about the timeline for enacting the legislation.
He said he wanted to do it as quickly as possible, but was also determined to get it right for women and for doctors.
Minister Harris said he hoped to publish a bill in the coming weeks and if at all possible to begin the debate.
However, he said it was not just about the law and there was also a need for clinical guidelines to be drawn up by practitioners and the regulation of medication in Ireland.
Martin to meet TDs, Senators over referendum result
The Fianna Fáil leader is to hold an individual meeting with each of his party's TDs and Senators to discuss the referendum result.
This follows a meeting of the Fianna Fáil parliamentary party in Leinster House tonight.
It is understood that the party leader called for unity of purpose and the importance of respecting the democratic will of the people to change the Constitution.
This view was echoed by Barry Cowen, the party’s spokesperson on Public Expenditure and Reform, who also said some had put their egos before the party during the referendum campaign.
This was interpreted by many in the room as a call to get all within the Fianna Fáil parliamentary party to back the legislation.
The meeting was described by some as not being divisive but the message was clear that TDs and Senators should fall into line.
However, it is understood that a number of TDs and Senators intend to abstain in any vote on the upcoming legislation and would oppose any suggestion of a party whip on the issue.
"There was nothing raw said but they are hinting that they want us to vote as a bloc," said one of those who attended the meeting.
Daly pays tribute to Yes side
In an emotional contribution in the Dáil this afternoon, Independents4Change TD Clare Daly said the weekend vote was "like an enormous weight being lifted".
She said: "I can't believe that I am 50 years of age, and it's taken my daughter to come home for her first vote to get us over the line"
She said the result was like society atoning for everything that has been done to women.
"Atoning for how we stigmatise women who face a crisis pregnancy, the Magdalene laundries, the Mother and Baby Homes, the shaming, the forced adoptions, the robbed identities that we're going to hear about later this afternoon, it still goes on," she said.
She said the biggest sentiment of the Yes vote, the thing that people said the most was "who am I to judge, it's not my decision".
She paid tribute to the people who fought the campaign for a yes vote, singling out Ailbhe Smyth of Together for Yes.
She acknowledged the contribution of Minister Harris, helped by Minister Katherine Zappone and Fine Gael TD Kate O'Connell.
However, she said politicians had not led on this issue.
"This has been an uphill battle, pushing a boulder up a hill over decades, and nobody in here was involved in pushing it up.
"Let’s be honest, nobody was involved. In actual fact, a lot of people in here were sitting on the boulder making it even more difficult for those outside who wanted to push for change."
Chair of the Oireachtas Health Committee Michael Harty has said that the committee is likely to sit during the summer to progress the legislation.
The medicines' regulator has said it will now accept applications to assess so-called abortion pills to be used in Ireland in the future.
In a statement to RTÉ's Morning Ireland, the Health Products Regulatory Authority said there was no medicine for the medical termination of pregnancy currently authorised in Ireland.
"Following on from the outcome of the referendum, the HPRA is open to receiving applications for medicines for the medical termination of pregnancy and will prioritise the assessment process."
This process involves a company submitting an application dossier containing "quality, safety and efficacy data."
"Should the review of this dossier result in a positive benefit-risk assessment, an authorisation for the medicine could be granted. We need all three things to happen concurrently," he added.
Elsewhere, Sinn Féin TD Peadar Tóibín, who also supported a No vote, has said he still opposed abortion on demand and would oppose legislation that allowed for it.
However, Mr Tóibín said that he would reserve his position on how he would vote on any legislation following the referendum on the Eighth Amendment until it had been published and scrutinised.
Additional reporting by Micheál Lehane