File Photo: The International Court of Justice ( ICJ ) during a hearing. Photo courtesy of ICJ website.
The Hague-based ICJ, the United Nations' top court, will open the public hearings after Ukraine lodged a complaint with the court to order Russia to stop its invasion.
"The hearings will be devoted to the request for the indication of provisional measures submitted by Ukraine," the court said in a statement.
More than 660,000 people have already fled abroad, the UN refugee agency said, estimating that a million people are displaced within ex-Soviet Ukraine, which has a population of 44 million.
The UN estimates that up to four million refugees may need help in the coming months and 12 million more will need assistance within the country.
The ICJ, which is based in the Netherlands' seat of government in The Hague, does not have a mandate to bring criminal charges against individual Russian leaders behind the invasion.
But it is the world's top court for resolving legal complaints between states over alleged breaches of international law.
International Criminal Court prosecutor Karim Khan had already announced he was launching an investigation on the "situation in Ukraine" following Russia's invasion.
"I am satisfied that there is a reasonable basis to believe that both alleged war crimes and crimes against humanity have been committed in Ukraine" since 2014, Khan said in a statement Monday.
Russia has defied international bans, boycotts and sanctions to press ahead with an offensive it says is aimed at defending Ukraine's Russian speakers and toppling the leadership.
The United States trusts "the Court is taking into consideration the dire circumstances and rapidly unfolding events," the State Department said in a statement Tuesday.
Spokesman Ned Price said Washington hopes the court "will act with utmost urgency on Ukraine's request for provisional measures" in the hearing.
"Each day that Russia is unconstrained in its aggression is a day that brings more violence, suffering, death, and destruction in Ukraine," he said.