The complicated interim ruling by 16 judges at the International Court of Justice in The Hague came as the conflict in eastern Ukraine enters its fourth year.
"Both parties shall refrain from any action which might aggravate or extend the dispute before the court or make it more difficult to resolve," the judges ordered.
More than 10,000 people have died in the fighting between pro-Moscow rebels and Ukrainian government forces since it erupted after the ouster of a Kremlin-backed regime in Kiev in February 2014.
Seeking to bring stability to its east, Ukraine had sought an urgent interim court order demanding Russia refrain from 'any action which might aggravate or extend the dispute' such as allegedly pumping money, weapons, equipment and personnel to the rebels.
And it urged the tribunal to order Moscow to control its borders with eastern Ukraine and halt racial discrimination in Crimea, particularly against Tatars, which Russia annexed in March 2014.
But the judges found that so far Kiev "has not put before the court evidence which affords a sufficient basis" to show that any funds from Moscow were used "to cause death or serious bodily harm to a civilian."
Therefore 'the conditions required for the indication of provisional measures' on whether Moscow had broken an international convention on terrorism financing 'are not met'.
However, they did agree with a second Ukrainian request to stop what Kiev called "racial discrimination" against minority groups in the Russian-occupied Crimea peninsula.
"The court is of the opinion that Crimean Tatars and ethnic Ukrainians in Crimea appear to remain vulnerable," said presiding judge Ronny Abraham, saying the court believed there was "an imminent risk" of "irreparable prejudice to the rights invoked by Ukraine."
Moscow must "refrain from maintaining or imposing limitations on the ability of the Crimean Tatar community to conserve its representative institutions," the judges ordered.
Russia must further 'ensure the availability of education in the Ukrainian language' on the peninsula.
The ICJ, which was set up in 1945 to settle disputes between countries in line with international law, has yet to decide whether it will take up the main case lodged by Kiev in January this year.
Moscow has denied Kiev's allegations that it has violated both the Terrorism Financing Convention and an international treaty against racial discrimination.
In its filing, Ukraine charged Russia with 'sponsoring terrorism' by financing pro-Russian separatists and failing to stop military aid from seeping across the border into eastern Ukraine's Donbas region.
It called on the court's 16 judges to rule that 'the Russian Federation bears international responsibility' for 'acts of terrorism committed by its proxies in Ukraine'.
These include the shelling and bombing of civilians and the downing of Malaysia Airlines flight MH17, shot down by a Russian-made Buk-missile over eastern Ukraine on July 17, 2014.
Ukraine wants Russia to pay compensation to all civilians caught up in the conflict, one of Europe's bloodiest since the 1990s Balkans wars, as well as to the families of the 298 victims of MH17.
But since it can take months for the ICJ to even decide to hear a case, Ukraine also sought interim protection measures, which were the basis for Wednesday's ruling.
Moscow has strongly denied Kiev's terrorism claims, saying they were 'neither factual nor legal' and argued that the ICJ does not have jurisdiction over the case.
The conflict has pushed ties between Moscow and the West to their lowest point since the Cold War.
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