The United Nations' top court on Wednesday mostly rejected Ukraine's claims that Russia was financing "terrorism" in eastern Ukraine, saying only that Moscow had failed to investigate alleged breaches.

Ukraine wanted Russia to compensate all civilians caught up in the conflict, as well as victims from Malaysia Airlines flight MH17, which was shot down over eastern Ukraine.

But the International Court of Justice (ICJ) tossed out most of Ukraine's claims, ruling only that Russia was "failing to take measures to investigate facts... regarding persons who have allegedly committed an offense".

The ICJ "rejects all other submissions made by the Ukraine", it said in a statement.