Alexander Zakharchenko, self-proclaimed prime minister of the Donetsk rebel area, said they had spent "four months on the territory of the Russian Federation".
But despite Zakharchenko's claims, there was no sign of the conflict widening after Kiev said it partially destroyed an armoured column that had crossed the border from Russia on Friday.
The report of the attack on the armoured column triggered a sell-off in the US dollar and European stocks, with markets fearful it could change the Ukraine conflict into an open confrontation between Moscow and Western-backed Kiev.
But Moscow made no threat of retaliation, instead saying it was a "fantasy" that its armoured vehicles entered Ukraine, while the White House said it could not confirm that Russian vehicles had been attacked on Ukrainian soil.
Speaking before Friday's incident, US officials said several options were under discussion if Russia did escalate the situation further. They include tightening sanctions, freezing Moscow further out of international forums, beefing up Nato's military presence in Eastern Europe and, perhaps, supplying more non-lethal aid.
Sanctions and economic pressure on Russia have prompted capital and expertise flight and a fully fledged trade war but no policy shift from Moscow.
On the ground, meanwhile, the conflict in eastern Ukraine yesterday continued, with reporters in Donetsk, one of two rebel strongholds in the east, saying explosions could be heard in the city centre.
The Finnish president, Sauli Niinisto, was due to arrive in Kiev this weekend for talks with Ukraine's president, Petro Poroshenko, aimed at finding a negotiated solution.
Niinisto had met Russian president Vladimir Putin in southern Russia on Friday and afterwards spoke of the possibility of a truce.
The United Nations said last week that an estimated 2086 people had died so far in the Ukraine conflict.
A rebel internet news outlet said yesterday that separatist fighters had killed 30 members of a Ukrainian government battalion in fighting in Luhansk province, a rebel-held area of eastern Ukraine.
Rebels said two villages south of Donetsk were bombed overnight with mortars. Rebel news outlet Novorossiya also said two neighbourhoods of the city itself had been hit with artillery.
A Ukrainian defence ministry spokesman, Andriy Lysenko, contradicted the rebel assertions. He said three Ukrainian servicemen had been killed over the past 24 hours, and denied Kiev's forces were firing artillery on Donetsk.
Lysenko said Ukrainian security forces had spotted Russian drones and a helicopter crossing illegally into Ukraine's airspace.
For the moment the momentum in the conflict on the ground is with the Ukrainian forces.
They have pushed the separatists out of large swathes of territory and have now nearly encircled them in Donetsk and Luhansk. Kiev says it controls the road linking the cities.
Russia says the Ukrainian offensive is causing a humanitarian catastrophe for the civilian population in the two cities. It accuses Kiev's forces of indiscriminately using heavy weapons in residential areas, an allegation Ukraine denies.