Fighters from the anti-Putin Russian groups that claim they made a cross-border attack into the southwestern Russian region of Belgorod on Monday heralded the raid, adding that their operation is "ongoing."
A member of the Freedom for Russia Legion who goes by the call sign "Caesar" told reporters Wednesday that the "effect of this raid was amazing."
The "whole internet [was] blowing up, boiling," Caesar told CNN while speaking to journalists who met with the fighters in the Sumy region of northeastern Ukraine.
Denis Nikitin, the commander of the Russian Volunteer Corps, said their operation continues. "Phase one, we consider it a successful phase. It's over now, but the operation is ongoing," he said.
Nikitin also commented on his group’s relationship with the Ukrainian military.
"Everything we do within the state borders of Ukraine, we obviously coordinate with Ukraine military," but "every decision we make behind beyond the border, behind the state border, is our own decision," he said.
"What we do, obviously, we can ask our, let's say, comrades, friends, for their assistance in planning," Nikitin said. "They will say 'yes,' 'no,' 'this is a good idea,' 'this is a bad idea.' So this is a kind of encouragement and help and aid."
The Ukrainian government has distanced itself from the Russian fighters, saying they are operating independently in Russia.
Legion fighter Caesar told journalists that Russian forces were "too stupid and too slow" in their response to the cross-border attack. He claimed his fighters destroyed a Russian mechanized company.
"We bring them heavy casualties," Caesar said.
The Russian Ministry of Defense claimed in a daily briefing on Tuesday that its forces repelled attackers back into Ukrainian territory using air strikes, artillery fire and military units.
When asked if Monday’s operation was part of the much-touted Ukrainian counteroffensive, Caesar said, "I think it is kind of, yes." He said the Ukrainian military provides the Freedom for Russia Legion with "small arms, artillery weapons, heavy vehicles, everything."
Asked about the overall goals of their mission, Caesar said: "We want to free our country ... live in, prosper in freedom, and have a capability to self-realization."