Russia has argued that the International Court of Justice (ICJ) lacks jurisdiction in Kyiv's case over Moscow's seizure of Ukraine's Crimea region and its support for separatists in eastern Ukraine.
The court in The Hague, Netherlands, on June 3 started holding public hearings in the case, with Russia's representatives vehemently rejecting Ukraine's allegations that Moscow supported terrorist activities in the conflict opposing Ukrainian government forces and Russia-backed separatists in the country's east.
Ukrainian representatives are to present Kyiv's arguments on June 4, and a second round of arguments will be held on June 6-7.
Moscow seized control of the Crimean Peninsula in March 2014 and has supported the separatists who control parts of the eastern Ukrainian regions of Donetsk and Luhansk in a war that has killed some 13,000 people since April of that year.
Ukraine filed the case at the ICJ in January 2017, accusing Russia of violating the International Convention for the Suppression of the Financing of Terrorism and the International Convention on the Elimination of All Forms of Racial Discrimination.
It said Moscow had stepped up its interference in Ukraine's affairs since 2014, "intervening militarily...financing acts of terrorism, and violating the human rights of millions of Ukraine's citizens, including, for all too many, their right to life."
The case also includes claims of Russian involvement in the downing of Malaysian Airlines flight MH17 by a missile over the conflict zone in July 2014.
Russia denies involvement in the tragedy in which all 298 people on board the aircraft were killed.
An international investigative team has determined that the Buk missile that struck the passenger jet came from Russia's 53rd Antiaircraft Missile Brigade and was fired from territory held by the separatists.
In The Hague, the Russian representatives told the ICJ that Kyiv failed to produce new evidence to show that Russia was involved in funneling arms and money to the separatists and in the downing of MH17.
"The case brought by Ukraine should be dismissed for lack of jurisdiction," Dmitry Lobach, a Russian ambassador-at-large, said.
In April 2017, the ICJ issued a provisional ruling calling for a halt to what it said was "racial discrimination" against Crimean Tatars and ethnic Ukrainians in Russia-occupied Crimea.
However, it rejected Ukraine's request to order Moscow to stop supporting separatists in eastern Ukraine.
The ICJ was set up in 1946 to rule in disputes between countries.