Russia was obviously supporting the militants in the Donbass region, while still pursuing a policy of plausible deniability.
And Kerry claims there is an enormous array of facts that Russia supported rebels, but remains vague. However, when checking the collection Wikipedia has made for the militants' war material, most of it appears to be stolen from military bases, captured, or even taken from museums. Wikipedias sources are incomplete, but the table doesn't list anything that can only have come from Russia.
The claim that Putin supports the rebels in eastern Ukraine is a rather strong one with profound political implications, so it deserves to be studied carefully.
What publicly available evidence is there for the claim that Russia supports the Donpass People's Militia?
Edit: By support, I mean that the national government of Russia provides direct support, in the form of money, training, by sending personnel, or otherwise, to the rebels. I am not skeptical of claims that Russian volunteers are fighting with the rebels.