The convoy was deployed a day after Ukrainian President Petro Poroshenko acknowledged that Russia would be part of an international humanitarian relief effort headed by the International Committee of the Red Cross.
Moscow, however, didn't wait for approval and coordination before unilaterally deploying 2,000 tons of humanitarian aid.
Ukraine and NATO have voiced concern that Russia would use a humanitarian mission as "an excuse to send troops into eastern Ukraine," further destabilizing the country.
On Monday, European Commission President Jose Manuel Barroso warned Russian President Vladimir Putin "against any unilateral military actions in Ukraine, under any pretext, including humanitarian."
Ukrainian officials said Tuesday that the Russian convoy would not be allowed to cross into Ukraine.
Andriy Lysenko, spokesman for Ukraine's National Security and Defense Council, said that the Russian trucks transporting the aid "belong to the military. International law forbids law enforcement services from accompanying humanitarian convoys."
Presidential Administration deputy head Valeriy Chaly commented on the tense situation from Kiev, declaring, "We do not consider any movement of Russian convoys on Ukrainian territory."
Instead, per the agreement with the Red Cross, both the Ukrainian branch of the Red Cross and personnel from Geneva would accept deliveries of aid at the border, process the aid through customs checkpoints and re-load the supplies onto other vehicles.
"We will not allow any escort -- either by the Russian Emergencies Ministry or any other law enforcement agency," Chaly said Tuesday.
The OSCE Special Monitoring Mission in Ukraine on Tuesday offered to assist the Red Cross with delivery of the humanitarian aid.