The International Committee of the Red Cross, which had planned to escort the convoy to assuage fears that it was being used as a cover for an invasion by Russia, said it had not received enough security guarantees to escort the convoy.
Trucks loaded with water, generators and sleeping bags sent from Moscow are intended for civilians in the city of Luhansk, where pro-Russian separatist fighters are besieged by government forces. Shelling of the city has been ongoing for weeks.
The vehicles' immediate destination was not known and it was not clear whether Kiev had granted its approval.
"The Russian side has decided to act," said a statement on the Russian foreign ministry's website. "Our column with humanitarian aid is starting to move in the direction of Luhansk."
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A rebel commander on the scene who identified himself only by the codename Kot said the trucks were headed for the city of Luhansk.
Shortly after leaving from the border town of Izvaryne, the convoy departed from the main road to Luhansk and headed north onto a country road and parked in the village of Uralo-Kavkaz. That route also leads to Luhansk, potentially avoiding areas controlled by government troops.
The trucks had been stranded in a customs zone for more than a week since reaching the border, as the Russian foreign ministry voiced increasing frustration at what it said were Kiev's efforts to stall its delivery.
A total of 34 Russian vehicles had received initial approved from Ukraine yesterday but were awaiting a final green light. But Russia's foreign ministry blasted the Ukrainian side for "endless, concocted delays" in delivering the aid, which left Moscow early last week.