DUBLIN, Ireland (CNN) -- Thousands of protesters marched through the streets of Dublin on Saturday to remember a woman who died after being refused an abortion and to demand a change to the country's laws.

Savita Halappanavar, 31, went into a hospital on Oct. 21 complaining of back pain. She was 17 weeks pregnant at the time.

The doctors who examined her told her she was having a miscarriage but denied her an abortion even though she was in extreme pain, her husband has said. Halappanavar died of septicemia, or a blood infection, at the hospital.

Chanting "never again, never again" protesters marched to government buildings and held a candlelit vigil in Dublin.

Vigils were also held other cities, including Galway, where Halappanavar died, and outside the Irish Embassy in London.

"I'm here today to stand up for women's rights. And I think the government should legislate and stop messing around," said Patrick O'Neill, a protester.

Abortions laws in Ireland are strict and terminations can only carried out in exceptional circumstances.

Twenty years ago, the Irish Supreme Court ruled abortions are allowed when there is a real and substantial risk to the life of the mother. But the ruling was never been enacted into law, meaning there is little clarity for doctors or patients as to when an abortion can and can't take place.

It is this Supreme Court ruling that some Irish people now want made into law.

Gerry Adams, leader of Ireland's Sinn Fein political party, has said it's time for the government to legislate for abortion in certain medical cases.

Other politicians have called called for an investigation into Halappanavar's death.

Her death is "particularly tragic and harrowing, and shocking to all concerned," said Irish opposition lawmaker Micheal Martin.

He has called for an independent inquiry into the case "with personnel from outside the country to participate on such a panel of inquiry." 

The Irish government needs to "establish the full circumstances" of her death, he said.

The government has said it will launch an investigation, but details, including who will lead it, remain elusive. The government has said it will include the Halappanavar family in the inquiry.

The hospital expressed sympathy to Halappanavar's husband, and noted in a statement that "the facts of this tragic case have yet to be established."

The hospital is conducting a review of the incident, as it does will all unexpected deaths. The Galway Roscommon University Hospitals Group released a statement saying, "In the case of a sudden maternal death, these procedures are followed: notification of the death to the coroner; notification of the death to the HSE's National Incident Management Team; the completion of a maternal death notification form. These national procedures are being followed by Galway University Hospital."

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