Ukraine blamed pro-Russian rebels, but they 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. Ukrainian forces have moved into the outskirts of rebel-held Luhansk, where basic supplies are running out.
Colonel Andriy Lysenko, a spokesman for Ukraine’s National Security Council, said he did not have an exact figure but that dozens of people had died, including children.
The barrage took place between the towns of Khryashchuvate and Novosvitlivka, which lie on the main road leading to Russia from the besieged rebel-held city of Luhansk, he said.
“Many people were killed, among them women and children,” Col Lysenko said. “We are not able to count the death toll at this point.”
When asked about a rough estimate of deaths, he replied: “Dozens.”
Another military spokesman said people had been burned alive inside their vehicles.
A 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. It seems they’ve now killed more civilians, like they’ve been doing for months now,” he said.
Fighting in eastern Ukraine has forced nearly 344,000 people to flee their homes, according to United Nations figures released on Friday. The UN says about 155,800 have left for places inside Ukraine while 188,000 have crossed into Russia.
The flow of refugees only seems to be growing. The UN Office for the Co-ordination of Humanitarian Affairs said more than 22,000 people had fled the main rebel-held city of Donetsk last week, compared with 6,200 the week before.
City officials have released even higher numbers. Donetsk has seen at least 300,000 of its pre-war population of one million leave their homes, while Luhansk has only 250,000 of its 420,000 people left, local authorities say.
Residents in Luhansk have had no running water, power or phone connections for 16 days. Basic foods are in short supply, leading to long queues outside shops, city authorities said yesterday, adding that fighting continued in and around the city.
The International Committee of the Red Cross (ICRC), which is expected to take responsibility for a Russian aid convoy when it enters Ukraine, has demanded security guarantees from all sides, including the rebels, for the mission into eastern Ukraine. However, yesterday there was no indication that the guarantees had been given.
The humanitarian aid convoy of more than 200 trucks from Russia has been watched with suspicion by Ukraine and the West. They suggest it could be used by Russia to send help to the separatists – or to delay the government’s advances with a timely ceasefire.
Russia’s foreign minister, meanwhile, said he expected the his country’s humanitarian aid mission to enter Ukraine soon.
Speaking yesterday at a news conference in Berlin, where he met a day earlier with his counterparts from Ukraine, France and Germany, Russian foreign minister Sergey Lavrov said that all questions regarding the mission had been answered and that an agreement had been reached with Ukraine and the ICRC.
It was not clear if Mr Lavrov was referring to the security guarantees.