Kiev has asked the International Court of Justice to "declare that the Russian Federation bears international responsibility, by virtue of its sponsorship of terrorism ... for the acts of terrorism committed by its proxies in Ukraine," the court said in a statement.
Ukraine also asked the court to order "full reparation" for the 2014 downing of flight MH17 over eastern Ukraine and "for the shelling of civilians" in certain towns in eastern Ukraine.
"The Russian Federation has been brutally violating international law for three years," he added in a statement.
"For three years, Russia has been committing the illegal annexation of Crimea, illegal occupation of the east of our country in the territory of Donetsk and Luhansk regions, implementing the policy of elimination and discrimination in Crimea."
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The International Court of Justice, the UN's highest court, was founded in 1945 to rule on border and territorial disputes between nations.
Fierce fighting flared in eastern Ukraine and Russia annexed Ukraine's southern peninsula of Crimea in March 2014.
There had been hopes the war was winding down after nearly the deaths of nearly 10,000 people after several ceasefire accords.
Poroshenko said the filing of the case at the ICJ had resulted from "a long and meticulous work."
Kiev has asked the tribunal to declare that Moscow has violated its obligations under the Terrorism Financing Convention and an international treaty against racial discrimination.
A Dutch-led international investigation found that Malaysia Airlines flight MH17 was shot down by a Russian-made missile in July 2014 over eastern Ukraine, launched from a field in rebel-held territory.
All 298 on board the routine flight from Amsterdam to Kuala Lumpur, mostly Dutch citizens, were killed.
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