The White House has urged Moscow to stop its "extremely dangerous and provocative" attempts to destabilise Ukraine, where tensions have soared again in the past 24 hours.
Ukraine says it has destroyed part of a Russian armoured column that entered on to its territory in an incursion that has sent cross-border tensions rocketing.
There has been an "escalation" in Russian activity in recent weeks to unsettle the already tense situation on the ground in eastern Ukraine, National Security Council spokeswoman Caitlin Hayden said in a statement on Friday.
"Even as we work to gather information (about the partial destruction of the Russian armoured column), we reiterate our concern about repeated Russian and Russian-supported incursions into Ukraine," Hayden said.
"Russia has no right to send vehicles, persons, or cargo of any kind into Ukraine, under any pretext, without the government of Ukraine's permission."
NATO also accused Russia of active involvement in the "destabilisation" of eastern Ukraine, where pro-Kremlin separatists have been fighting against Kiev for four months.
Russia and neighbouring Ukraine have been wrangling for days over a convoy that Moscow says is carrying humanitarian aid for besieged rebel-held cities but which Kiev suspects could be a "Trojan horse" to provide military help to the insurgents.
But Russia's Defence Minister Sergei Shoigu "guaranteed" his US counterpart Chuck Hagel that there were "no Russian military personnel involved in the humanitarian convoy, nor was the convoy to be used as a pretext to further intervene in Ukraine," the Pentagon said.
Fears that the border clash could spill into all-out war between Kiev and Moscow sent major share markets tumbling across Europe and the United States.
Ukrainian President Petro Poroshenko told British Prime Minister David Cameron that government artillery had destroyed a "considerable part" of a small military column that entered the country, the presidency said in a statement.
The European Union demanded that Russia "put an immediate stop to any form of border hostilities, in particular to the flow of arms, military advisers and armed personnel into the conflict region, and to withdraw its forces from the border."
German Chancellor Angela Merkel voiced that view in a phone call on Friday with Russian President Vladimir Putin.
Moscow's defence ministry dismissed the alleged military column as a "phantom", its latest denial of Western accusations that it is funnelling weapons to the pro-Russia separatists who launched an insurgency against Kiev in April.
But NATO chief Anders Fogh Rasmussen backed reports of the "Russian incursion" after British media said it had seen the column of some 20 military vehicles cross the border on Thursday.
"It just confirms the fact that we see a continued flow of weapons and fighters from Russia into the eastern Ukraine," he said.
As the fallout snowballed, Ukraine's foreign minister announced he will meet his Russian counterpart Sergei Lavrov in Berlin on Sunday for talks alongside the top diplomats from France and Germany.
"Be it a square table or a round one, we need to talk," minister Pavlo Klimkin wrote on Twitter.
Russia's foreign ministry ominously accused Ukraine of "attempts to derail the supply of humanitarian aid" as doubts swirled over what will happen next to almost 300 Russian trucks parked up some 30 kilometres from Ukraine's border.
It had appeared earlier that the two countries might reach a deal to allow the convoy into Ukraine to help people in the east who are without water, food or power.
But the International Committee of the Red Cross said they were still ironing out details over the shipment.