Nadia Murad was 21 years old when, she says, Islamic State fighters abducted her, beat her and raped her. Her offense: belonging to the minority Yazidi community, whom the Islamic State regards as infidels. Her cause for the last two years: demanding justice for the Islamic State’s atrocities.

This week, Ms. Murad clinched a small, but important victory. Her country, Iraq, agreed to let the Security Council appoint a panel of independent investigators to gather evidence of the most serious crimes committed by the Islamic State, and not just those against Yazidis. Lacking that, the Security Council would have had to adopt a resolution to create such a panel.

Still to be resolved is where and how those crimes will be prosecuted, and how to make sure those trials are credible and not displays of victor’s justice.

Ms. Murad’s quest poses an acute test for the promise of international justice, born from the ashes of Nazi genocide 70 years ago, after World War II.

If the most powerful countries in the world cannot hold accountable those who are accused of enslaving women for sex, beheading their perceived enemies, turning children into suicide bombers and carrying out what an international panel believes could be an act of genocide against the Yazidi people, what is the very notion of international justice good for?

The Islamic State, also known as ISIS, is accused of some of the gravest crimes known to humanity, and not only against the Yazidis. It does not have powerful countries defending it, as does say, the government of Syria, which also stands accused of a raft of war crimes.

Not least, the Islamic State committed these atrocities at a time when the world has a set of firmly established laws and a permanent International Criminal Court in The Hague precisely to deter and punish those who commit such crimes.

The I.C.C. has no jurisdiction in Iraq, though; the nation is not a member of the court, and there is no appetite on the Security Council’s part to refer the conflict in Iraq to the court.

In early August, the United Nations-authorized Commission of Inquiry urged world powers to recognize the crime of genocide against the Yazidis and to “undertake steps to refer the situation to justice.” Yet, even with that, the effort to investigate — let alone prosecute — those crimes has not been so straightforward.

The Security Council has the power to dispatch investigators to collect evidence or to set up a special tribunal. But it was reluctant to do either without Iraq’s consent.

That consent came Wednesday. In a letter to the United Nations, Iraq’s foreign minister, Ibrahim al-Jaafari, said his government would work with the British government on a draft Security Council resolution seeking “international expertise to criminalize” the Islamic State. The political sensitivities were clear in his letter. Mr. al-Jaafari emphasized Iraq’s “sovereignty and jurisdiction” in adopting any such resolution.

Translation: Iraq is wary of letting international investigators pry into crimes on its territory, which could potentially implicate its own forces or allies.

Amal Clooney, a British lawyer and rights activist who represents Ms. Murad, said she welcomed Iraq’s consent for an international investigation, as a first step.

“Yazidis and other ISIS victims want justice in a court of law, and they deserve nothing less,” Ms. Clooney said in a statement Wednesday. “I hope that the Iraqi government’s letter will mark the beginning of the end of impunity for genocide and other crimes that ISIS is committing in Iraq and around the world.”

Justice, of course, means different things to different parties.

Iraq has arrested thousands of suspected Islamic State members under its counterterrorism laws, which include the death penalty for membership in a banned terrorist group.

Islamic State fighters are facing trials in domestic courts from Tunisia to Germany to Iraq, although it remains to be seen how or where the group’s most senior leaders will be tried for the most serious international crimes, including genocide.

Trying such crimes in local courts can be tricky. “Most significantly,” said Balkees Jarrah, senior counsel with Human Rights Watch, “political will to permit independent and impartial criminal prosecutions can be in short supply in countries affected by conflict.”

Ms. Murad, now 24, is barely five feet tall. She does not smile much, and she rarely veers away from her prepared remarks, in Arabic. She favors solid black tunics and shoes made for walking. She sometimes looks as though she would rather be doing anything other than recounting for well-dressed, influential world leaders the horrors she lived through.

She has met with the Canadian prime minister, the queen of Jordan, United States ambassadors (representing both the Obama and Trump administrations), two successive secretaries general of the United Nations and, on several occasions, halls of dignitaries and philanthropists.

She has told and retold her awful story. The man who first came for her. “A monster,” is how she described him. Her brothers being executed. Mass graves.

And as time goes on, and she finds herself telling and retelling her story, it becomes harder for her to contain her fury.

At a briefing in the Security Council earlier this year, she looked up from her notes at one point and snapped, in halting English, at a room full of hushed diplomats from the world’s most powerful countries. “What more you need before you will act?” she asked bluntly.

She was honored last year with a human rights prize in honor of the Czech dissident Vaclav Havel. The United Nations appointed her a good will ambassador. Her memoir, “The Last Girl: My Story of Captivity, and My Fight Against the Islamic State,” is to be published this fall by Tim Duggan Books, an imprint of Crown Publishing Group.

Ms. Murad, who now lives in Germany, says she never wanted this life. She was a farmer’s daughter. She wanted to open a beauty salon.

Her discomfort at being a crusader comes out sometimes. In an interview last fall, she confessed to being worn out, but also unable to give up.

“I will go back to my life when women in captivity go back to their lives, when my community has a place, when I see people accountable for their crimes,” she said.