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
A Malaysian court has found a man guilty of murdering two British medical students in Borneo.
A Liberal Democrat parliamentary candidate has said he deliberately caught HIV after years battling depression.
Noel Edmonds beat off competition from Ant and Dec to be voted Britain's favourite children's TV presenter.