The refugees were being escorted by the Ukrainian military out of the towns of Khryaschuvate and Novosvitlivka when they came under fire.
"Many people have been killed, including women and children," National Security and Defense Council spokesman Andriy Lysenko reported.
According to Lysenko, the militants used weapons provided by Russia, including mortars and Grad rockets, to attack the convoy as it traveled on a road east of Luhansk.
The Ukrainian military is in the midst of an anti-terrorist operation to retake control of parts of eastern Ukraine occupied by Russian-backed militants, and has established humanitarian corridors to facilitate the evacuation of civilians.
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