Health authorities in Ireland have begun investigating the death of a woman who died in hospital after being repeatedly refused an abortion.

Savita Halappanavar was 17 weeks into her pregnancy when she was admitted to hospital last month, suffering agonising back pain and miscarrying.

Her family says the 31-year-old asked for an abortion several times before she died of blood poisoning.

But staff at University Hospital Galway told her even though she was Hindu, she was in a Catholic country, and they could not induce her because there was a foetal heartbeat.

Halappanavar died on October 28, one week after entering hospital. An autopsy found she died from septicemia. The foetus had been removed on October 23 after its heartbeat stopped.

Abortion is illegal in the Republic except when the mother's life is at risk.

Halappanavar's husband, Praveen Halappanavar, says he has no doubt his wife would have lived if she was allowed to have an abortion.

"Savita was really in agony. She was very upset, but she accepted she was losing the baby," Mr Halappanavar, 34, told the Irish Times from southern India, where his wife's funeral took place.

"When the consultant came on the ward rounds on Monday morning, Savita asked if they could not save the baby, could they induce to end the pregnancy.

"The consultant said, 'As long as there is a foetal heartbeat, we can't do anything.'

"Again on Tuesday morning, the ward rounds and the same discussion. The consultant said it was the law, that this is a Catholic country.

"Savita said: 'I am neither Irish nor Catholic', but they said there was nothing they could do."

Halappanavar was a Hindu originally from India. She and her husband lived in Galway, where he worked as an engineer.

"The fact that this young woman lost her life is a personal tragedy and a family tragedy. No words of ours here can deal with that loss," prime minister Enda Kenny told parliament on Wednesday.

He said the health minister had asked for a report, while investigations had been launched by the hospital and by Ireland's Health Service Executive.

Mr Kenny said he would not pre-judge the inquiries but stressed: "It is very important and imperative that the standards that apply in our maternity units be kept at the very highest level of professionalism and competence".

'Very frightening'

Protesters hold pictures of Savita Halappanavar as they demonstrate outside parliament in Dublin. ( AFP: Peter Muhly )

The news of Mrs Halappanavar's death sparked a wave of anger on Irish social media, with more than 50,000 people sharing the Irish Times' lead story on the issue.

More than 2,000 people later rallied outside parliament to demand that the country's strict abortion laws be eased.

"My reaction was outrage. [It's a] shame that this happened in my country," protester Emer McNally, 33, who is six months pregnant, said.

"It's scary to think that medical treatment was denied."

In the absence of legislation, Irish women are forced to go abroad to terminate their pregnancies, an option not open to seriously ill mothers.

"It's very frightening. It makes me feel it's not a safe country in which to have a baby," Sinead O'Brien, a 41-year-old holding a placard saying 'Never Again', said.

"There has been a groundswell of feeling all day. I think something has to change."

The organisers of the Dublin protest say they expect a much larger crowd at a weekend demonstration and have called on people to protest at Irish embassies around the world.

Despite a dramatic waning of the influence of the Catholic Church, which dominated politics in the country until the 1980s, successive governments have been loathe to legislate on an issue they fear could alienate conservative voters.

After several challenges, the European Court of Human Rights ruled in 2010 that Ireland must clarify its position.

ABC/wires