Updated at 1:20 p.m. ET.
Ukraine's president says Kiev's artillery destroyed a "significant" part of a Russian armored column that is said to have crossed the border overnight.
Russia called the claim a "fantasy."
President Petro Poroshenko told British Prime Minister David Cameron that Ukrainian forces had hit the column, according to the presidential website. Separately, a Ukrainian military spokesman said the Russian column of armored personnel carriers were tracked as they crossed the border. "Appropriate actions were undertaken and a part of it no longer exists," military spokesman Andriy Lysenko told journalists, according to Reuters.
Earlier, NATO Secretary-General Anders Fogh Rasmussen said the alliance observed a "Russian incursion" overnight, confirming that Moscow was continuing to supply pro-Moscow separatists with "a continuous flow of weapons and fighters."
"Last night we saw a Russian incursion, a crossing of the Ukrainian border," Rasmussen told reporters after meeting the Danish defense minister, according to Reuters.
"It just confirms the fact that we see a continuous flow of weapons and fighters from Russia into eastern Ukraine, and it is a clear demonstration of continued Russian involvement in the destabilization of eastern Ukraine," said.
Russia's Defense Ministry has denied that any of its forces crossed the border.
"There was no Russian military column that crossed the Russian-Ukrainian border either at night or during the day," the ministry was cited as saying in a statement, according to Reuters. The Russians dismissed the Ukrainian report as "some kind of fantasy."
The remarks came as a Russian convoy purportedly carrying humanitarian aid to eastern Ukraine had been halted near the border as it awaited inspection by officials concerned that it could be a pretext for invasion.
Bloomberg says: "The incursion last night isn't seen by Ukraine as a new development or a possible start of an invasion by Russia, Defense Ministry spokesman Leonid Matyukhin said by phone. The vehicles were painted white to camouflage the operation as a peacekeeping mission, he said. The military column, which wasn't part of Russia's convoy delivering humanitarian aid, rolled into insurgent-held territory, Andriy Lysenko, a spokesman for the military, told reporters in Kiev today."
Meanwhile, NPR's Soraya Sarhaddi Nelson, at the eastern border with Russia, says Ukrainian officials reportedly have begun inspecting the convoy at a border crossing that leads to Luhansk, an area where fighting between pro-Russia separatists and Kiev's forces has been ongoing.
Karoun Demirjian, reporting for NPR from Moscow, says the inspections are taking place on the Russian side of the border.
The Associated Press says Moscow has agreed to the procedure and to allow the Red Cross to distribute the aid.
In a statement from the International Committee of the Red Cross on Friday, spokesman Laurent Corbaz said the relief organization would deliver the aid to health centers in the area inside Ukraine where fighting was taking place. He urged both sides to agree quickly to moving the aid to where it's needed.
"We still need assurances from all parties to the conflict that our staff will be allowed to perform their tasks safely and with due respect for our humanitarian principles," he said.
Karoun reports that European diplomatic officials and some journalists in the area first reported that some Russian military vehicles did cross into Ukraine overnight and that two British newspapers said "at least 23 Russian military vehicles" were involved.