"Ukraine is, today, a slaughterhouse. Right in the heart of Europe," Clooney told an informal UN Security Council meeting on accountability in Ukraine, organised by France and Albania.
Clooney recalled a 2017 Security Council vote to approve a measure she helped lobby for - the creation of a UN team to collect, preserve and store evidence of possible international crimes committed by Islamic State in Iraq.
It was the same year her son and daughter with US actor George Clooney were born.
"My children are now almost five, and so far most of the evidence collected by the UN is in storage - because there is no international court to put ISIS on trial," she said.
The International Criminal Court, which handles war crimes, crimes against humanity, genocide and crimes of aggression, has no jurisdiction because Iraq and Syria are not members.
Clooney is part of an international legal task force advising Ukraine on securing accountability for Ukrainian victims in national jurisdictions and working with the Hague-based ICC.
ICC Prosecutor Karim Khan opened an investigation into the situation in Ukraine a week after Russia's February 24 invasion.
"This is a time when we need to mobilise the law and send it into battle," Khan told the UN meeting.
"Not on the side of Ukraine against the Russian Federation, or on the side of the Russian Federation against Ukraine, but on the side of humanity."
Russian diplomat Sergey Leonidchenko described the ICC as a "political instrument."
He accused the United States and Britain of hypocrisy for supporting the ICC inquiry in Ukraine after doing "everything imaginable to shield their own military".
Moscow describes its February 24 invasion of Ukraine as a "special military operation" and denies targeting civilians.
Ukrainian Prosecutor General Iryna Venediktova's office has told Reuters it is preparing war crimes charges against at least seven Russian military personnel.
