KIEV, Ukraine >> Ukraine on Monday accused pro-Russia separatists of killing dozens of civilians in an attack on a convoy fleeing a besieged rebel-held city. The rebels denied that any attack took place, while the U.S. confirmed an attack but said it did not know who shelled the convoy.

The war zone in eastern Ukraine is effectively off limits for the journalists and lacks power in many places, limiting citizens from easily providing their own reports. All this makes independent verification impossible.

Fighting between government troops and pro-Russian separatists in Ukraine has forced nearly 350,000 people to flee their homes, according to the United Nations. The flow of refugees from eastern Ukraine has been rising steadily as the humanitarian situation in rebel-held cities deteriorates. Running water and electricity have either been cut off completely in cities like Luhansk or are getting more limited by the day.

The rebels shelled the convoy of refugees Monday morning between the towns of Khryashchuvate and Novosvitlivka with Grad rockets and other weapons imported from Russia, Col. Andriy Lysenko, a spokesman for Ukraine’s National Security Council, told reporters.

The towns lie on the main road leading into Russia from the rebel-held city of Luhansk.

“Many people were killed, among them women and children,” Lysenko said. “We are not able to count the death toll at this point.”

When asked about a rough estimate of deaths, he said “dozens.”

Oleksiy Dmytrashkivsky, a spokesman for the Ukrainian government’s military operation in the east, later told The Associated Press that 15 bodies had been recovered from the smoldering vehicles and servicemen were collecting the body parts of at least ten more people.

Yet Donetsk rebel chief Alexander Zakharchenko insisted that no such attack had taken place. His deputy, Andrei Purgin, said he had no information about an attack and insisted it was not by his forces.

“If someone was killed, it wasn’t us but the Ukrainian military,” Purgin told the AP.

The road where Ukraine said Monday’s attack took place had been targeted previously by government forces, Purgin said.

That same road to Luhansk would likely be the route taken by a controversial Russian aid convoy if Ukraine allows it into the country.

The United States offered its condolences to the families of those killed Monday.

“We strongly condemn the shelling and rocketing of a convoy that was bearing internally displaced persons in Luhansk and express our condolences to the families of the victims,” U.S. State Department spokeswoman Marie Harf told reporters in Washington. “All sides must take every precaution to protect innocent lives. We are unable to confirm reports of who was responsible for the shelling and rocketing.”

Fighting across eastern Ukraine has forced nearly 344,000 people to flee their homes, according to U.N. figures released Friday. And the flow of refugees only seems to be growing. The U.N. Office for the Coordination of Humanitarian Affairs said more than 22,000 people fled the main rebel-held city of Donetsk last week compared to 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 1 million leave their homes, while Luhansk has only 250,000 of its 420,000 people fled, 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 lines outside shops, the city hall said Monday, adding that fighting continues in and around the city.

In Donetsk, the largest city in rebel hands, several houses were hit by artillery fire over the weekend in the Budyonovsky district, which stands next to a rebel encampment.

One house was still smoldering when an Associated Press reporter visited Monday. The rocket hit the yard and set fire to a tree, which in turn set several nearby buildings ablaze. The fire destroyed the cramped, one-story home of Nina Saltanova, 79, and her paralyzed 56-year-old daughter.

Asked if she wanted to leave the city, she despaired.

“I have nowhere to go, my daughter is disabled,” Saltanova said, salvaging scraps of clothing from the charred debris. “She can’t walk. Because of her I can’t go anywhere.”

Tensions have been high in the past week as Russia decided to send a massive aid convoy to help those in rebel-held eastern Ukraine.

The over 200 trucks from Russia, now parked in a Russian field by the border, have been watched with suspicion by Ukraine and the West, especially since Ukrainian forces have been winning back significant territory from the rebels in the last few weeks. Ukraine suggests the aid convoy could be used by Russia to send help to the separatists — or to delay the government’s advances with a timely cease-fire.

The International Committee of the Red Cross, which is expected to take responsibility for the Russian convoy when it enters Ukraine, said on Monday it was still waiting for security guarantees from all sides for the mission into eastern Ukraine.

Russia’s foreign minister, meanwhile, said in Berlin that he expects the Russian aid mission to enter Ukraine in the near future.

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Peter Leonard in Donetsk, Ukraine, Yuras Karmanau in Minsk, Belarus, Juergen Baetz in Brussels, Matt Lee in Washington, Jim Heintz and Lynn Berry in Moscow contributed to this report.