Minister for Health James Reilly has asked the HSE to report to him once the executive has completed its investigation into the circumstances surrounding the death of Savita Halappanavar.
Ms Halappanavar, who was 17 weeks pregnant, died at University Hospital Galway following a miscarriage.
Her husband said that his wife had asked for a medical termination before she died on 28 October.
It is reported that Ms Halappanavar, 31, presented with back pain at the hospital on 21 October and was found to be miscarrying her baby.
Her family said she asked several times over a three-day period that the pregnancy be terminated.
It is reported that this was refused, because the foetal heartbeat was still present.
Dr Reilly described Ms Halappanavar's death as a terrible tragedy, and offered his sympathy to her family.
He said a report from an expert group on abortion chaired by Judge Seán Ryan had been delivered to his department last night, and he would have to study that carefully before deciding on what steps to take next.
Meanwhile, over 1,000 people protested at Leinster House this evening to demonstrate in favour of abortion legislation in the wake of Ms Halappanavar's death.
Taoiseach - 'Tragic coincidence'
Taoiseach Enda Kenny has described as a tragic coincidence the death of Ms Halappanavar and the Government's receipt of the expert group's report.
Mr Kenny said people will inevitably link the two issues when in reality they were quite separate.
He told journalists that Dr Reilly now had to study the report and bring conclusions to Government, while separately enquiries into the death of Ms Halappanavar would proceed.
Junior Health Minister Kathleen Lynch has said the circumstances that led to Ms Halappanavar's death cannot be allowed to continue.
She said that action must be taken to ensure that people in the medical profession have the security and guidelines on what to do in such circumstances.
The coroner has been informed about the results of the post mortem examination on Ms Halappanavar's body.
In a statement, the Galway Roscommon University Hospitals Group said it will co-operate fully with the coroner’s inquest.
"The review has not yet started as the hospital is waiting to consult with the family of the deceased on the terms of reference," it said.
Calls for independent inquiry
Fianna Fáil leader Micheál Martin said Ms Halappanavar's death was tragic and harrowing.
Mr Martin said Ireland had always aimed for a low death rate during pregnancy and he said this was cold comfort to the woman in question.
He said an independent inquiry was needed, with personnel from outside the country to establish the full circumstances.
An internal inquiry will not suffice, he said.
Mr Martin said that considering the enormity of what happened, he believed an exceptional response was called for.
Sinn Féin's Gerry Adams said there was an onus on the Government to bring forward its plans for legislation on these issues.
The Supreme Court, he said, had ruled that a termination would be lawful if the life of the mother was in danger.
The people had placed responsibility for such legislation in the hands of the Government, he said.
Northern Ireland MLA Anna Lo said the death of Ms Halappanavar shows the need for clarity on the law around abortion in the Republic and Northern Ireland.
Ms Halappanavar celebrated baby shower
Speaking to RTÉ's News at One, Praveen Halappanavar said his wife had gone to their GP and "everything was ok" three or four days before she presented at the hospital back pain.
Mr Halappanavar said the couple were told that their baby was "perfectly alright" and was due on 30 March.
He said his wife was "on top of the world" and they had celebrated a babyshower with their family.
Mr Halappanavar said that on the night of Saturday 21 October, his wife could not sleep due to back pain.
He said the couple called the hospital at 9am the next morning and were told to come in.
Following a series of checks the couple went home, but Mr Halappanavar said that the couple returned to the hospital at around 11am when Savita felt there was something wrong.
Mr Halappanavar requested that his wife be seen by a doctor and he was told that there was a cervical dilation and that they did not think the baby would survive.
He said he was told it would all be over in four or five hours and that his wife could then go home.
At the time Mr Halappanavar said that his wife was not in severe pain, but was suffering discomfort as a result of some back pain.
Mr Halappanavar said that on Tuesday night things started to get much worse, with his wife feeling cold and "shivering terribly".
On Friday morning, one of the midwives urged him to tell Savita's parents that their daughter was now critically ill.
Mr Halappanavar said the hospital tried dialysis, and gave her platelets to see if it could improve her condition.
At around 1am on Sunday 28 October, he was asked if he would like to sit with his wife during her final moments.
He said "the nurse came running I was just standing outside ICU. She just told me to be brave and she took me near Savita and she said: 'Will you be OK to be there during her last few minutes?' I said 'Yes I want to.'"
Mr Halappanavar, who is currently in India, said he will be returning to Ireland soon.
He said his father-in-law is very ill and is in severe shock following the news of his daughter's death.