Kiev filed the case shortly after hostilities began on February 24, accusing Russia of illegally justifying its war by falsely alleging genocide in Ukraine's Donetsk and Luhansk regions.
Russia has not attended a hearing at the UN's top court where Ukraine asked for an immediate halt to Moscow's invasion.
The no-show to Monday's hearing was criticised by the head of the International Court of Justice (ICJ), and by Ukraine which said the empty Russian seats "speak loudly".
"The court regrets the non-appearance of the Russian Federation in these oral proceedings," ICJ President Joan Donoghue said.
Ukraine wants the court to take provisional measures ordering Russia to "immediately suspend the military operations", pending a full judgment in the dispute that could take years.
"The fact that Russia's seats are empty speaks loudly. They are not here in this court of law, they are on a battlefield, waging aggressive war against my country," Ukraine's representative Anton Korynevych told the court.
"This is how Russia solves disputes."
"Russia must be stopped, and the court has a role to play in stopping that," he added.
Russia had been scheduled to give its reply on Tuesday.
Kiev filed the case shortly after Vladimir Putin's February 24 invasion, accusing Russia of illegally justifying its war by falsely alleging genocide in Ukraine's Donetsk and Luhansk regions.
The court set two days for urgent hearings at the Peace Palace in The Hague but Russian ambassador Alexander Shulgin wrote to the court and "indicated that his government did not intend to participate".
'Russia planning acts of genocide in Ukraine'
The ICJ was set up after World War II to rule on disputes between UN member states, based mainly on treaties and conventions.
Its rulings are binding but it has no real means to enforce them.
This case hinges on the 1948 UN Convention on Genocide, to which both Ukraine and Russia are parties.
The ICJ was already dealing with a dispute between the two countries dating back to Russia's 2014 annexation of Crimea and support for pro-Moscow rebels in Donetsk and Luhansk.
Ukraine says Russia has now wrongly invoked the genocide convention with an "absurd lie" about genocide of Russian-speakers in Luhansk and Donetsk.
"Russia's lie is all the more offensive, and ironic, because it appears that it is Russia planning acts of genocide in Ukraine," it said in its court filing.
Experts said Ukraine's effort to drag Russia to the world court over the invasion could have symbolic value, though it was unclear if Moscow would heed any order.