The Government has published the Protection of Life during Pregnancy Bill after it was approved by Cabinet.
These include a provision giving the Minister for Health power to suspend institutions deemed to be operating the Act inappropriately.
The minister will also publish an annual report setting out how many terminations have been carried out.
Other changes include expanding the number of hospitals allowed carry out terminations.
It will also broaden the category of psychiatrist allowed decide whether a pregnant woman's life is at risk from suicide.
Tánaiste Eamon Gilmore welcomed the Bill’s publication saying, "if this Bill is passed, every one of the tens of thousands of pregnant women who are admitted to hospital every year will know that any action which may be needed to save her life in an emergency will be taken.
"If this Bill is passed there will be no need for worry, no reason for doubt on the part of the woman, her family or the medical professionals concerned," he said.
Minister for Health James Reilly briefed the Fine Gael parliamentary party at Leinster House.
Party chairman Charlie Flanagan said the meeting was calm and constructive.
He said the minister went into some detail about the contents of the legislation.
He said concerns were expressed, some of which were addressed and a number of members do have difficulties with what is proposed.
Mr Flanagan said the Bill will be introduced to the House next Thursday.
TDs and Senators said they received assurances about the possibility of regular Oireachtas scrutiny of the workings of the Act.
One TD said Mr Reilly answered all the questions put to him and was very assured.
There will be no guillotine used and a period for reflection will be allowed before committee stage.
The Bill will be back to the Dail on 11 July and extra sitting days will be allowed if necessary.
There will be no "sunset clause", as sought by some Fine Gael backbenchers, under which the legislation would lapse by a certain date unless renewed.
One doctor will be required to certify that a termination is justified in the case of medical emergencies.
Two doctors will have to certify where there is a physical threat to the life of the mother, and three in cases of suicidal ideation.
Those three doctors will include the woman's obstetrician and two psychiatrists, including one specialist with experience of dealing with the mental health of pregnant women.
Ipsos/MRBI poll shows majority in favour of legislation
An opinion poll to be published tomorrow shows that three quarters of voters approve of the Government legislation.
However, the Ipsos/MRBI poll for the Irish Times found a smaller proportion - 52% in favour of allowing abortion in cases of threatened suicide.
1,000 voters were polled on Monday and Tuesday.
Asked if they approved of the Heads of the Bill published by the Government, allowing for abortion where a woman's life is at risk, an overwhelming majority, 75% said yes, with 11% undecided.
But when asked if they approved of abortion on the grounds of a threat of suicide, one of the provisions of the legislation, only 52% said they did, with 29% opposed and 19% undecided.
There was higher support for abortion in other circumstances; 89% where a woman's life is at risk, 83% where the foetus cannot survive outside the womb, 81% in cases of rape or incest, and 78% where there was a threat to the health of the woman.
But where a woman claims an abortion is in her best interests, just 39% would support an abortion, with 46% opposed.
Taoiseach says legislation provides clarity
Taoiseach Enda Kenny said the Cabinet discussions had been constructive and coherent.
He earlier defended the legislation and said he is a Taoiseach who happens to be a Catholic, rather than a Catholic Taoiseach.
Speaking in the Dáil, he said the Government will act strictly in accordance with its Constitutional obligations and inside the law.
He said he was providing certainty and clarity and said that the legislation is about saving lives not ending them.
Mr Kenny said he is being branded by some people as a murderer who will have the death of 20 million babies on his soul.
He has received medals, scapulars, plastic foetuses, letters written in blood and telephone calls, he said.
The Taoiseach was speaking in response to independent TD Mattie McGrath, who said the Government is proposing abortion legislation that will fundamentally change the law.