The new draft, which will bring clarity to the country's stringent anti-termination laws, forms part of the changes promised by the government after Savita's death.
"I do hope that we can bring everybody with us, on an issue that I know is sensitive," Prime Minister Enda Kenny told reporters in Dublin after his government published the Protection of Life During Pregnancy Bill.
Calling on Catholic conservatives within his own party to back the bill or be expelled, he stressed that the government was seeking only "a clarification of rights within existing law".
The current law, dating to 1861, sets the maximum penalty at life.
More From This Section
The new bill, which will have to be passed in both houses of the Irish Parliament, will allow for limited legal termination where there is a threat to the mother's life.
Savita, 31, was 17 weeks pregnant when she was admitted to University Hospital Galway last year and died of blood poisoning four days after delivering a dead foetus.
An inquest into her death last month was told that her two requests for termination were turned down on the grounds that Ireland is a "Catholic country".
The Cabinet had finally reached a shaky consensus on the draft earlier today.
The new law would mean that hospitals will have clear, legal guidelines when they considered such requests for an emergency termination.
The historic bill has deeply divided the Kenny government as some Catholic conservatives within his party have vowed to reject the bill.