Dozens of women in Greenland have heard Denmark's prime minister, Mette Frederiksen, formally apologise for a scandal that involved thousands of Inuit women being forcibly given contraceptive coils, as part of a controversial birth control programme during the 1960s and 70s.

Dear women. Dear families. Dear Greenland. Today there is only one right thing to say to you. Sorry, Frederiksen told a packed venue in the centre of the capital Nuuk.

During an emotionally charged event, one woman stood with her back to the prime minister in protest, a black handprint painted across her mouth.

Sorry for the injustice that was committed against you, Frederiksen said. Because you were Greenlanders. Sorry for what was taken from you. And for the pain it caused, she continued. On behalf of Denmark. Sorry.

Naja Lyberth, who was one of the first of the Inuit Greenlanders to speak out about what happened, received a standing ovation as she addressed Wednesday's event.

If we are to move forward, the apology is crucial, she said.

An official inquiry earlier this month concluded that at least 4,000 women had a coil implanted by 1970, corresponding to roughly half the Greenlandic females of childbearing age.

In more than 300 cases examined by the inquiry, women and girls as young as 12 had been fitted with an IUD without their knowledge or consent.

Welcoming Frederiksen's apology and the investigation, Naja Lyberth was also critical that it had not explored possible human rights violations.

Frederiksen acknowledged that many women had lived with trauma and physical complications, and that some were not able to have children.

Among the women named by the prime minister in her speech was Elisa Christensen, who listened to the leader's words carefully and found her apology very overwhelming.

Although she said she was still taking it in, she told the BBC: There was no mention of compensation at all we are sad about that. It was almost like empty words.

A lawsuit demanding compensation has been filed by a group of 143 women.

Greenland was a Danish colony until 1953, and then became a county of Denmark, before gaining home rule in 1979. However, Copenhagen oversaw the healthcare system until 1992, when Greenland took over responsibility.

Frederiksen's apology comes amid increased scrutiny of Denmark's relationship with Greenland, and growing international pressure, particularly following President Donald Trump's repeated demands to take control of the Arctic territory.

The IUD case is one of several historic and current controversies, including forced adoptions, that have damaged Danish-Greenlandic relations. Most recently, another flashpoint has involved the removal of Inuit children from their families following parenting competence tests.

This week, a decision by Danish authorities to separate a young Greenlandic mother from her newborn daughter - one hour after she gave birth - was reversed after the case prompted outrage.

For Elisa Christensen, Denmark's official apology has brought a rollercoaster of emotions. The little girl inside me, for the first time she felt she got a little hug from society.

But for the grown-up Elisa, I don't know [how] I use that apology. Where are the children and grandchildren I should have?