Ukraine has asked the court to order Russia to "immediately suspend the military operations" launched on February 24 "that have as their stated purpose and objective the prevention and punishment of a claimed genocide" in the separatist eastern regions of Luhansk and Donetsk.
Lawyers for Kyiv dismissed the Russian claim.
"Ukraine comes to this court because of a grotesque lie and to seek protection from the devastating consequences of that lie," David Zionts told the court. "The lie is the Russian Federation's claim of genocide in Ukraine. The consequences are unprovoked aggression, cities under siege, civilians under fire, humanitarian catastrophe, and refugees fleeing for their lives."
A decision on Ukraine's request is expected within days. The court's president, American judge Joan E. Donoghue, said the judges would issue a decision "as soon as possible".
If the court were to order a halt to fighting as Ukraine requested, "I think the chance of that happening is zero," said Terry Gill, a professor of military law at the University of Amsterdam. He noted that if a nation does not abide by the court's order, judges could seek action from the United Nations Security Council, where Russia holds a veto.
Donoghue said Russia's ambassador to the Netherlands, Alexander Shulgin, informed judges that "his government did not intend to participate in the oral proceedings".
Because of Russia's refusal to participate in the hearings, Moscow's turn to present legal arguments on Tuesday was canceled.
Korynevych condemned Moscow's snub.
"The fact that Russian seats are empty speaks loudly," he said. "They are not here in this court of law. They are on a battlefield waging aggressive war against my country."
The request for so-called provisional measures is linked to a case Ukraine has filed based on the Genocide Convention. Both countries have ratified the 1948 treaty, which has a clause allowing nations to take disputes based on its provisions to the Hague-based court.
"Ukraine emphatically denies that any such genocide has occurred and that the Russian Federation has any lawful basis to take action in and against Ukraine for the purpose of preventing and punishing genocide," the country said in its claim to the court.
Even before the hearing, Donoghue sent a message to Russia's foreign minister on March 1 pressing home the necessity to act "in such a way as will enable any order the Court may make on the request for provisional measures to have its appropriate effects".
Jonathan Gimblett, a member of Ukraine's legal team, highlighted the urgency of Ukraine's case, saying Moscow's "military aggression could have resulted in a new nuclear catastrophe affecting not only Ukraine or Russia, but potentially a vast surrounding area".
He added that Russia, "today is resorting to tactics reminiscent of medieval siege warfare, encircling cities, cutting off escape routes and pounding the civilian population with heavy ordnance".
The success of Ukraine's request will depend on whether the court accepts it has "prima facie jurisdiction" in the case, which is not a guarantee that the court ultimately would proceed with the suit. Cases at the International Court of Justice typically take years to complete.
Regardless of the outcome of the hearings, they give Ukraine another platform to air grievances about Moscow's invasion.
"It's part of, I think, an overall diplomatic strategy to try to put maximum pressure on Russia," said Gill.
Ukrainian representative Oksana Zolotaryova emotionally underscored the high stakes as the hearing closed.
"As I am speaking, the Russian Federation continues its relentless assaults on our cities, on our towns, on our villages, on our people," she told judges.
She added: "We don't know yet the true number of Ukrainians that Russia has murdered in the past eleven days. We can only guess how many more will be murdered in the next eleven days if this senseless aggression does not stop."
US assures nervous Baltics of Nato protection
Meanwhile, US Secretary of State Antony Blinken assured Lithuania and Latvia of Nato protection and American support as he made quick visits to two of the three Baltic states that are increasingly on edge as Russia presses ahead with its invasion of Ukraine.
Along with Estonia, which Blinken will visit on Tuesday, the former Soviet republics are Nato members, and the Biden administration is aiming to calm any fears they have about their security in the event Russia chooses to expand its military operations.
In the Latvian capital of Riga, Blinken said the Baltics have "formed a democratic wall that now stands against the tide of autocracy" that Russia is pushing in Europe.
"The United States is more committed than ever to standing with you as our democracies rise to the challenge.
"We are bolstering our shared defense so that we and our allies are prepared."
He stressed that the U.S. commitment to Nato's mutual defense pact is "sacrosanct" and that Nato and the United States were discussing the permanent basing of troops in the Baltics.
— AP