Ukrainian authorities have said that trucks from a Russian aid convoy crossed into Ukraine without permission and Ukraine's state security chief said this amounted to a "direct invasion" by Russia, news agencies have reported.
"They passed into Ukraine without clearance or participation of the International Red Cross or [Ukrainian] border guards," military spokesman Andriy Lysenko told journalists.
"We consider this a direct invasion by Russia of Ukraine," Ukrainian state security chief Valentyn Nalivaychenko said in a separate statement to journalists, according to Reuters news agency.
He added that Ukraine would not use force against the convoy "to avoid provocations".
The United States and European Union said the decision was a violation of Ukraine's border.
"This is a violation of Ukraine's sovereignty and territorial integrity by Russia," Rear Admiral John Kirby, the Pentagon press secretary, told a briefing.
"Russia must remove its vehicles and its personnel from the territory of Ukraine immediately. Failure to do so will result in additional costs and isolation."
"This is a clear violation of the Ukrainian border and goes counter to the previous arrangements reached between Ukraine, Russia and the ICRC (International Committee of the Red Cross)," Sebastien Brabant, spokesman for the European Union's foreign policy chief Catherine Ashton, said.
"We urge Russia to reverse its decision."
Earlier on Friday, Russia said it was no longer prepared to tolerate any delays to the aid convoy heading for Ukraine and that the trucks were starting to move towards Luhansk, where pro-Russian rebels are fighting Ukrainian government forces.
At least 90 trucks crossed the border into eastern Ukraine on Friday, Reuters reported. It is thought they are being escorted by pro-Kremlin separatists and have now entered Luhansk.
The trucks are loaded with water, generators and sleeping bags intended for civilians of the besieged city, where pro-Russian separatist fighters are besieged by Ukrainian forces.
"All excuses to delay sending aid... have been exhausted. The Russian side has taken the decision to act," the Russian foreign ministry said in a statement on Friday, warning against any attempts to disrupt the convoy's movement.
More than 200 trucks had been held at the border zone over Ukraine's concerns that Russia had not complied with International Red Cross rules regarding humanitarian aid.
The ICRC confirmed it was not escorting the convoy, citing the "volatile security situation" in the region. It had previously been a stipulation of the aid transfer that the ICRC would coordinate the distribution and travel with the trucks.
The relief supply mission is proceeding despite both sides in the conflict ignoring pleas for a ceasefire.
Several of the vehicles had been cleared by both countries' customs authorities on Thursday and were waiting for the green light to enter Ukraine from an ICRC team that had been overseeing the operation.
Ukraine has expressed repeated fears that Russia may be using the vehicles to smuggle in weapons to pro-Kremlin rebels who have been battling government forces for more than four months.
Russia has consistently denied that it is arming separatist rebel groups operating in the eastern cities of Luhansk and Donetsk.
Meanwhile, Ukraine's armed forces say they have caused heavy casualties among pro-Russian separatist forces, although their overall advance quelling the rebel resistance remains haphazard and faltering.
Defence officials said on Friday in a daily update that government forces had destroyed 11 Grad missile systems, three tanks and five armoured personnel carriers during fighting near the town of Snizhne.
They also claimed to have killed about 100 rebel fighters.
The claims could not immediately be verified and Ukrainians have in the past made overblown estimates of their successes.