The case of a woman denied an abortion at an Irish hospital who later died of blood poisoning must prompt the state to loosen its almost total ban on terminations, a member of one of the coalition parties in Dublin has said.

Two investigations – one by Ireland's health executive, the other by the hospital – are now under way into the circumstances of the death of the 31-year-old dentist at University Hospital Galway (UHG) who was denied a medical termination and allegedly told: "This is a Catholic country."

Savita Halappanavar's death has highlighted how the ban even can prevent women with life-threatening medical conditions getting an abortion in Irish hospitals.

She had turned up at UHG on 21 October and was found to be miscarrying but died of septicaemia a week later. She had asked medical staff several times over a three-day period to terminate the pregnancy.

An Irish Labour deputy in the Dáil, Patrick Nulty, said that in light of Halappanavar's death there was "pressing and urgent need" for parliament to "show responsibility and legislate", calling on his party and its Fine Gael partners to press ahead with reforming the abortion law.

It is understood her family is now considering taking legal action, arguing that the foetus should have been removed earlier to save the woman's life.

Her husband, Praveen Halappanavar, said her repeated requests were turned down because she was 17 weeks pregnant and staff could detect a foetal heartbeat. The 34-year-old engineer has since revealed that his wife spent two and a half days "in agony" until the foetal heartbeat stopped.

After the dead foetus was removed, he said, his wife was taken to the hospital's intensive care unit where she died on 28 October.

Recounting her final days in UHG, he said: "Savita was really in agony. She was very upset, but she accepted she was losing the baby. 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 [an Indian Hindu] said: 'I am neither Irish nor Catholic,' but they said there was nothing they could do.

"That evening she developed shakes and shivering and she was vomiting. She went to use the toilet and she collapsed. There were big alarms and a doctor took blood and started her on antibiotics.

"The next morning I said she was so sick and asked again that they just end it, but they said they couldn't."

He recollected the moment he heard that medical staff were moving his wife into intensive care.

"They said they were shifting her to intensive care. Her heart and pulse were low, her temperature was high. She was sedated and critical but stable. She stayed stable on Friday but by 7pm on Saturday they said her heart, kidneys and liver weren't functioning. She was critically ill. That night, we lost her."

The hospital said it could not discuss the details of an individual patient with the media but expressed its sympathy to the family.

A spokesman for the hospital, which is part of a group of medical centres in western Ireland, said: "Galway Roscommon University Hospitals Group (GRUHG) co-operates fully with coroners' inquests. In general, in the case of a maternal death, a number of procedures are followed, including a risk review of the case and the completion of a maternal death notification form.

"External experts are involved in the review and the family of the deceased are consulted on the terms of reference, are interviewed by the review team and given a copy of the final report."

The taoiseach, Enda Kenny, said he would not be rushed into any measures while the two independent inquiries were under way.

His health minister, James Reilly, is understood to have received a report meanwhile from a group of experts exploring the possibility of reforming Ireland's abortion laws. Women who have had terminations in England for medical reasons called on Reilly on Wednesday to publish the findings as soon as possible in the light of Savita Halappanavar's death.

"I think it would be only appropriate that the two investigations that are being carried out here are concluded," Kenny said.

At present the coalition government is preparing a report on possible legal reforms of abortion legislation in the light of a European court ruling in 2009 that declared the absolute ban to be a breach of women's human rights.

Nulty, TD for Dublin West, said: "The heartbreaking tragedy of the death of Savita Praveen Halappanavar is something which should cause every citizen in our republic to pause and reflect."

He added that the government should no longer "hide behind reports and delay tactics. It must act to protect women and their health. This issue cannot be swept aside and ignored as successive governments have done."

Intervention by the European court of human rights has forced Ireland to make some minimal changes to its abortion ban. Since the 1992 X case, in which a 14-year-old rape victim took on the state's ban not only on her having a termination in Ireland but also on her travelling abroad for an abortion, there have been some exceptional circumstances.

Since Europe ruled that there was a risk to the child's life if she was forced to go ahead with the pregnancy, guidelines have been set down on these rare and exceptional cases.

Ireland's Medical Council guidelines state that "abortion is illegal in Ireland except where there is a real and substantial risk to the life (as distinct from the health) of the mother".

It adds: "Under current legal precedent, this exception includes where there is a clear and substantial risk to the life of the mother arising from a threat of suicide."

The guidance also informs doctors that they "should undertake a full assessment of any such risk in light of the clinical research on this issue".

And it advises that "rare complications can arise where therapeutic intervention (including termination of a pregnancy) is required at a stage when, due to extreme immaturity of the baby, there may be little or no hope of the baby surviving.

"In these exceptional circumstances, it may be necessary to intervene to terminate the pregnancy to protect the life of the mother, while making every effort to preserve the life of the baby."

However, such decisions are often left to the discretion of individual doctors and their medical teams. The pressure group Terminations for Medical Reasons Ireland, which campaigns for women whose babies would die if they went full term into their pregnancies, points out that in many cases some Irish doctors will not even advise women on their rights to travel abroad for abortions, let alone recommend emergency terminations in Ireland.