The United States has urged Russia to stop what it says is "extremely dangerous and provocative" attempts to destabilize Ukraine.
In an August 15 statement, White House spokeswoman Caitlin Hayden warned Moscow that intervention into Ukraine without permission from Kyiv is unacceptable.
She said there had been an "escalation" in Russian activity in recent weeks to destabilize the situation in eastern Ukraine.
The White House said it cannot confirm reports that Ukraine had destroyed armored vehicles that were part of a Russian convoy that had entered Ukraine late on August 14.
It said "Russia has no right to send vehicles, persons, or cargo of any kind into Ukraine" without permission from the Ukrainian government.
Ukrainian President Petro Poroshenko said earlier on August 15 that Ukrainian forces had destroyed part of a Russian armored column that crossed the border the previous night.
The presidential press service said Poroshenko, in a telephone conversation on August 15, told British Prime Minister David Cameron that information carried by British media that Russian APC's had crossed the border was "trustworthy" and "confirmed that a significant part of the equipment" had been destroyed by Ukrainian artillery.
A Ukrainian military spokesman said Ukrainian forces had tracked the Russian armored column as soon as it crossed into Ukraine.
There was no information from Ukrainian officials on the whereabouts of the rest of the convoy.
Earlier on August 15, NATO Secretary-General Anders Fogh Rasmussen said the alliance had observed a Russian "incursion" into Ukraine.
Rasmussen, speaking on a visit to Copenhagen, said the incursion occurred overnight in a "clear demonstration of continued Russian involvement in the destabilization of eastern Ukraine."
But the Russian Defense Ministry denied that Ukrainian forces had destroyed a Russian military column, saying the Ukrainian report is "some kind of fantasy."
The Russian Foreign Ministry also accused Ukraine of attempting to disrupt the delivery of Russian humanitarian aid to eastern Ukraine.
The ministry accused Kyiv of stepping up military operations with the "obvious goal" of blocking the agreed route of the aid convoy.
Reporters for two British newspapers reported on August 14 seeing about 23 Russian armored personnel carriers (APCs) cross into Ukraine after joining with the humanitarian convoy.
Russia says the convoy of around 280 trucks is carrying water, food, and other aid for people in eastern Ukraine, where Ukrainian forces are fighting pro-Russian separatists.
Western officials have expressed concern it could be a pretext for a military incursion.
Russia said Foreign Minister Sergei Lavrov is continuing talks with his Ukrainian counterpart, Pavlo Klimkin, on practical issues related to the deliveries.
Earlier, officials said an understanding had been reached between Russia, Ukraine, and the International Committee of the Red Cross (ICRC) regarding the mission.
Ukrainian officials said dozens of Ukrainian border guards and customs officers crossed into Russia to inspect the convoy.
ICRC official Laurent Corbaz, who is currently in Kyiv, said the ICRC would itself deliver the aid but had still not received security guaranties "from all parties to the conflict."
Finnish President Sauli Niinisto, who met with Russian President Vladimir Putin in Sochi on August 15, said he hoped a Russian humanitarian aid delivery would pave the way for a cease-fire between the government and the pro-Russian separatists.
EU foreign ministers meeting in Brussels on August 15 said the European Union would consider any unilateral military action by Russia in Ukraine as a blatant violation of international law.
Klimkin said he and Russia's Lavrov will meet alongside the top diplomats from France and Germany in Berlin on August 17.
The Kremlin press service said the Russian and the Ukrainian chiefs of presidential staff met in Russia on August 15. It said Sergei Ivanov and Borys Lozhkin, respectively, "discussed a wide range of issues."