Clooney, who represents Yazidi women who escaped from IS enslavement, was addressing UN member-states for the second time in six months to appeal for action to prosecute IS militants.
"Why is it that nothing has been done?" Clooney told the gathering.
"Mass graves lie unprotected and unexhumed. Witnesses are fleeing and not one ISIS militant has faced trial for international crimes anywhere in the world," she said.
The Lebanese-British lawyer said a British-drafted resolution setting up the investigation was ready to be submitted to the Security Council, but that Iraq had yet to give its approval for the measure.
Britain is leading a push for accountability for the crimes of IS - who seized control of large parts of Syria and Iraq in mid-2014 - declaring its Islamic caliphate and committing widespread atrocities.Clooney called on Iraqi Prime Minister Haider al-Abadi to "send the letter to the Security Council requesting the investigation into ISIS crimes."
Amal Clooney, Barrister at Doughty Street Chambers and Legal Representative for Nadia Murad and other Yazidi survivors. Source: AAP
"Don't let ISIS get away with genocide," she urged.
Iraq's Ambassador Mohamed Alhakim said his government was committed to ensuring justice and that Iraqi courts had received 500 cases involving IS crimes.
With Iraqi forces beating back IS fighters in Mosul, Alhakim said that the next step would be ensuring a "true reconciliation" among the city's religious and ethnic groups.
"We need these communities to be at peace with each other," he said.
Iraq launched the offensive in October to retake Mosul, which fell to the Islamic State group amid resentment by the local Sunnis towards Shiite-dominated security forces.