Amal Clooney and Nadia Murad are calling out the United Nations' failure to bring Islamic State fighters to justice, urging the international body to start tracking down the perpetrators of genocide and put them on trial.

In searing speeches at United Nations headquarters in New York on Thursday, Ms. Clooney, the high-profile human-rights lawyer, and Ms. Murad, a Yazidi woman enslaved by IS in 2014, said there is no excuse for the UN's inaction.

"Don't let this be another Rwanda, where you regret doing too little, too late," said Ms. Clooney, who represents Yazidi victims of IS. "Don't let ISIS get away with genocide," she said, using an acronym for the Islamic State group.

Story continues below advertisement

Related: 'Our people have been suffering': Vulnerable Yazidis urge Canada for aid

While an international coalition of countries has provided military support to groups in Iraq and Syria fighting IS, the UN has so far made no attempt to document the group's crimes against humanity or to mete out justice to the perpetrators, she said.

And the longer it waits, the harder it will be to collect the evidence necessary to secure convictions.

Britain last year drafted a resolution that would see the UN Security Council set up an investigation into IS.

But Ms. Clooney said all parties have sat on their hands and not pushed the resolution forward.

Iraq, despite endorsing the resolution publicly, has failed to send the letter to the Security Council requesting an investigation that would trigger a vote on the resolution and the Security Council has failed to order an investigation on its own or refer the matter to the International Criminal Court.

The General Assembly or the Secretary-General could also set up investigations, but they have also not done this.

Story continues below advertisement

"I am speaking to you, the Iraqi government, and to you, UN member states, when I ask: Why? Why has nothing been done?" Ms. Clooney said.

She said there is no reason for the UN not to act: Not only is IS a brutal force, but it has no powerful country blocking UN action on its behalf. IS is so sure of its own impunity, she said, that it is leaving piles of evidence – including mass graves – because it knows no UN investigators are bothering to document them and prosecute anyone.

"What is shocking here is not just the brutality of ISIS but how long those who know about it can remain passive. If we do not change course, history will judge us, and there will be no excuse for our failure to act," she said.

IS has particularly singled out the Yazidis, a religious minority in northern Iraq that it aims to wipe out. Canada last month agreed to take in 1,200 Yazidis by the end of this year.

Ms. Murad, who was captured by IS fighters who slaughtered all the men in her village, managed to escape after months of enslavement. She said several members of her family – including a three-year-old niece – remain enslaved. Some Yazidi boys captured by IS are forced to become suicide bombers, she said.

"I am deeply disappointed that my words, my tears, my testimony seem to have failed to make you move against ISIS. I wonder, should I continue this campaign of mine? Will it be of any use?" she said, appearing to hold back tears. "I spoke at the United Nations the first time 15 months ago and since then no ISIS fighters have been brought to justice for their collective crimes against my society."

Story continues below advertisement

Since her escape, Ms. Murad has become a human-rights activist, been named UN Goodwill Ambassador for the Dignity of Survivors of Human Trafficking and won the Vaclav Havel Human Rights Prize last year.

And IS has continued to threaten her, she said, adding that the government of Germany, where she now lives, has had to give her personal protection to ensure her safety. Every time she speaks out, she said, she puts her family in danger.

But she said the UN has not shown enough urgency and is "letting ISIS get away" with its crimes.

"For over a year, the victims have patiently awaited the beginning of this investigation against ISIS to be able to at least bury our dead. But why is it taking so long? I cannot understand why you are letting ISIS get away with it, or what more you need to hear before you act," she said.

Ms. Clooney pointed out that the UN itself recognizes IS treatment of the Yazidis as genocide – but even this has not been enough to get it to lift a finger.

"The UN was created as the world's way of saying 'never again' to the genocide perpetrated by the Nazis," Ms. Clooney said. "And yet here we are, 70 years later, discussing the UN's inaction in the face of a genocide that we all know about, and that is ongoing."