Savita Halappanavar went to Galway University Hospital on 21 October complaining of back pain. After routine tests the young mother-to-be was told everything was fine and was sent home.
When she returned later that day, doctors found she was miscarrying.
Praveen Halappanavar told The Irish Times his wife, who was 17 weeks pregnant, asked for a medical termination several times over a three-day period.
Although she was in severe pain at the time, her husband said the 31-year-old dentist's requests were denied because a foetal heartbeat was still present.
Mr Halappanavar claimed they were told: "This is a Catholic country."
His wife was later transferred to intensive care as her condition deteriorated. She died of septicaemia in the early hours of Sunday 28 October - a week after she first visited the hospital.
I was holding her hand, they were trying to pump her heart; there was a big team around. The doctor just told me they lost her.
Praveen Halappanavar, speaking to RTÉ
Mrs Halappanavar's death is being investigated by the Galway-Roscommon University Hospitals Group and the state's health officials and it is expected to be completed within three months.
The hospital said in a statement: "It is standard practice to review unexpected deaths in line with the HSE's national incident management policy."
A spokesman expressed sympathy to the family and friends of Mrs Halappanavar and said it is normal for medics to tell the coroner and Health Service Executive about the death, as well as completing a maternal death notification.
"The family of the deceased is consulted on the terms of reference, interviewed by the review team and given a copy of the final report," he said.
The spokesman added that the hospital was waiting to consult Mrs Halappanavar's family on the terms of reference before beginning the review.
In a statement, the Department of Health said: "The department and the ministers extend their sympathies to the family of the patient on their loss.
"There are currently two investigations underway and the department is awaiting the completion of these investigations before commenting further."
A pro-choice protest was held in front of the Dáil on Wednesday evening, after left-wing TDs described the woman's death as an outrage.
Reforms proposed in the Irish Parliament earlier this year would have introduced new laws to allow an abortion in specific life-threatening circumstances. But the government failed to adopt the X Case Bill introduced by Clare Daly and Joan Collins.
"This is a situation we were told would never arise. An unviable foetus - the woman was having a miscarriage - was given priority over the woman's life, who unfortunately and predictably developed septicaemia and died," said Independent TD Ms Daly.
A woman has died because Galway University Hospital refused to perform an abortion needed to prevent serious risk to her life.
Taoiseach Enda Kenny would give no indication as to whether he would introduce laws allowing women to have a termination in certain life-threatening circumstances.
Sinn Féin leader Gerry Adams asked Mr Kenny when he intended to legislate for abortion, while Fianna Fáil leader Micheál Martin called for an external inquiry to be carried out by Government.
Mr Kenny extended his sympathies to the family.
"A child has been lost, a mother has died and a husband is bereaved," he said.
"That is a tragedy."
"I don't think we should say anything about this until we are in possession of all the facts," he added.
In Northern Ireland, the death has prompted calls for guidelines on terminations to be made clear.
Alliance MLA Anna Lo said the lack of clear guidelines has created "uncertainties and confusion amongst medical staff".
"I hope that the Health Minister Edwin Poots is looking at what happened to Savita and takes action. He needs to stop dragging his feet over the publication of the guidance to enable doctors to avoid any possible confusion and ensure that they work properly according to the law," the south Belfast representative said.
Mr Halappanavar took his wife's body back to India to be cremated and laid to rest.