Around 70 Russian aid trucks have now entered Ukraine without permission from Kiev and the previously agreed escort of the Red Cross, Reuters reports.
An unnamed Ukrainian government official told the news agency: "The convoy started to move on its own, without consent from the Ukrainian side and unaccompanied by the Red Cross."
Russian President Vladimir Putin has reportedly been informed of the convoy's progress.
More top news
Nick Clegg has insisted on more education spending in any coalition deal. But has he learned his lesson since the tuition fees fiasco?
Burnley have banned 21 people for life following violent scenes after a Championship match last season.
Anis Abid Sardar is alleged to have made the roadside bombs which killed Sergeant first class Randy Johnson in Iraq in 2007.