RTÉ News has learned that in the case of suicidal ideation, for a woman to be granted a termination of pregnancy, the three consultants reviewing the case must all agree that this should proceed.
There is provision for an appeal by the woman where termination of pregnancy is not approved by the first three doctors.
That appeal would be to three other consultants.
The appeal panel of three doctors must also be unanimous in approval for a termination to be granted under law.
The procedures mean that in the case of suicide threat, a woman could have six doctors reviewing her application.
The full details of the legislation are due to be published later this evening.
One Cabinet source said there had been substantial changes to the measures.
They told RTÉ News that it was a very different Bill to the legislation described in earlier media reports.
Some Fine Gael sources said they were hopeful that backbenchers with misgivings about including the risk of suicide as grounds for abortion might think differently when they see the terms of the legislation.
The adjournment came after what Cabinet sources described as a lengthy discussion of the legislation.
Taoiseach Enda Kenny denied there were any problems at Cabinet with the legislation and ministers dealt with 28 items this morning.
He earlier said it was the Government's intention to have the heads of the bill sent to the Oireachtas Health Committee after approval today.
It is now 21 years since the Supreme Court judgment in the X Case, which found that abortion was legal under the Constitution, if there was a real and substantial risk to the life of the mother.
The court held that this included the threat of suicide.
The draft heads will go for detailed discussion in the Oireachtas Health Committee, before the actual legislation is drawn up and introduced in the Dáil.
There is significant opposition to the measure within Fine Gael, with several TDs and Senators likely to defy the party whip on the issue.
Mr Kenny has urged opponents to study the wording, and contribute to the debate, before coming to a final decision.