A Ukrainian military spokesperson says dozens of people, including women and children, died when their convoy of buses was hit by rocket fire while they were trying to flee the eastern city of Luhansk.
Ukraine has accused pro-Russian rebels of targeting the convoy, which it said was bearing white flags when it was hit.
The rebels have denied carrying out the attack near the village of Novosvitlivka. A rebel news outlet reported a heavy exchange of artillery fire in the area, the BBC reported.
Ukrainian Military spokesman Andriy Lysenko said "militants" armed by Russia had fired at a refugee convoy fleeing the city of Luhansk with mortars and Grad rockets.
He said "dozens" of civilians had died, including women and children.
"The convoy had white flags and was marked as civilian," Mr Lysenko said.
Another military spokesman said people had been burned alive inside their vehicles.
But the spokesman for the rebel self-proclaimed "Donetsk People's Republic", Andrei Purgin, denied that rebel forces had attacked the convoy.
"The Ukrainians themselves have bombed the road constantly with planes and Grads. It seems they've now killed more civilians like they've been doing for months now," he was quoted as saying.
Alexander Zakharchenko, a rebel leader in Donetsk, told journalists: "Not a single convoy of refugees was shot at in the Luhansk region."
Under siege
There has been sustained artillery shelling of Luhansk, a city of 250,000 people, where civilians are suffering chronic shortages of water, food and electricity. Before the conflict, the population was closer to 420,000.
Hundreds of civilians are fleeing the city every day as Ukrainian forces edge into Luhansk.
The key rebel-held town of Horlivka near Donetsk has been encircled, military officials say, in another sign that the separatists have lost ground in recent days.
More than 2,000 civilians and combatants have been killed since mid-April, when Ukraine's government sent troops to put down the rebel uprising in the east.