Ukraine has said that it will not allow any Russian aid into the country if it is accompanied by the Russian military or members of Russia's emergencies ministry.
Referring to a Russian convoy dispatched this morning with aid to Ukraine, presidential aide Valery Chaly said: "This cargo will be reloaded onto other transport vehicles [at the border] by the Red Cross.
"We will not allow any escort by the emergencies ministry of Russia or by the military [onto Ukrainian territory]. Everything will be under the control of the Ukrainian side."
The Russian convoy of 280 trucks carrying humanitarian aid set off amid Western warnings against using help as a pretext for an invasion.
With Ukraine reporting Russia has massed 45,000 troops on its border, NATO said there was a "high probability" that Russia could intervene militarily in the country's east, where Ukrainian forces are closing in on pro-Russian separatists.
Western countries believe that Russian President Vladimir Putin could now send his forces into the east to head off a rebel defeat.
Itar Tass news agency said the convoy departed from near Moscow, which means it would take it a couple of days to arrive in east Ukraine, 1,000km to the southwest.
"It has all been agreed with Ukraine," Business FM radio quoted President Putin's spokesman, Dmitry Peskov, as saying.
Thousands of people are believed to be short of water, electricity and medical aid due to the fighting.
US President Barack Obama said that any Russian intervention without Ukraine’s consent would be unacceptable and violate international law.
European Commission President Jose Manuel Barroso also warned "against any unilateral military actions in Ukraine, under any pretext, including humanitarian".
Russian state television Rossiya 24 showed several heavy white trucks departing from the town of Alabino near Moscow.
A Rossiya 24 correspondent at the scene said the convoy should arrive at the Ukrainian border in two or three days where it would meet a representative of the International Committee of the Red Cross (ICRC).
Russia has said the aid would be delivered together with the ICRC.
The ICRC said yesterday it had submitted a document to Russian and Ukrainian officials.
However, the independent agency said that it needed agreement from all parties as well as security guarantees to carry out the operation, as it does not use armed escorts.
"The practical details of this operation need to be clarified before this initiative can move forward," said Laurent Corbaz, head of ICRC operations for Europe and Central Asia.
According to UN agencies, more than 1,100 people have been killed including government forces, rebels and civilians in the four months since the separatists seized territory in the east and the government in Kiev began its crackdown.