The statement on the Russians by Colonel Andriy Lysenko, a spokesman for Ukraine's National Security Council, came after the country's defence minister said Ukraine's armed forces are expanding their strategy from just fighting separatists to facing the Russian army in a war that could cost "tens of thousands" of lives.
Col Lysenko said Russian troops had been seen in the cities of Donetsk and Luhansk, as well as other locations throughout the east. The claim could not be confirmed independently. Col Lysenko also said 15 Ukrainian servicemen had been killed on Monday.
In Moscow, a Kremlin aide criticised EU Commission president Jose Manuel Barroso for breaching confidentiality when he quoted Russian president Vladimir Putin as saying that Moscow could take over Kiev in two weeks if it wished.
Yuri Ushakov, the Russian leader's foreign policy adviser, said Mr Putin's statement was "taken out of context and carried a completely different meaning".
Mr Ushakov lashed out at Mr Barroso, saying it was a breach of diplomatic practices and "unworthy of a serious politician" to speak publicly about a private conversation.
Mr Barroso had briefed the EU's 28 leaders hours after the phone conversation at a summit in Brussels - from where the information eventually leaked.
Mr Putin's comment reportedly came in response to Mr Barroso pointing out Ukrainian and Western reports that Russia had sharply escalated the conflict in eastern Ukraine by sending regular army units into Ukraine.
Nato estimates at least 1,000 Russian soldiers have entered Ukraine, helping turn the tide in the last week in favour of the pro-Russian insurgents. The military alliance also says 20,000 other Russian soldiers have been positioned along the Ukraine-Russian border.
Mr Ushakov reaffirmed Moscow's repeated denial it has sent any soldiers into Ukraine, even though a rebel leader said last week Russian servicemen on leave were among some 4,000 Russians fighting in Ukraine.
Ukrainian defence minister Valeriy Heletey said the counter-insurgency operation against the rebels was over and the nation's military was now facing the Russian army.
"This is our Great Patriotic War," he wrote, using the local terminology for the Second World War.
Russia's foreign ministry dismissed Mr Heletey's remarks as "shocking" and accused him of trying to shift blame and keep his position amid a series of defeats suffered by the Ukrainian military.
Pro-Russian rebels have been fighting Ukrainian government troops since mid-April in a conflict that has left more than 2,500 people dead and forced at least 340,000 to flee. In the last week, the rebels have scored significant gains on the ground, launching a new offensive along the Sea of Azov coast.
Efforts to negotiate a peaceful settlement to the hostilities, which followed the ousting of Ukraine's pro-Russian president and Russia's annexation of Crimea in March, have failed.