With thousands now dead, Ukraine refugees say aid is welcome but peace is ...

Zhanna Sologub doesn't know if the rocket that struck the courtyard of her house this month was fired by pro-Russian rebels or Ukrainian government forces.

What she does know, she said, is that the biggest humanitarian gesture either side could make right now is to stop the fighting.

Amid intensifying battles this past week for control of key cities in eastern Ukraine, Russia prepared to distribute food, medicine and other supplies that it delivered to rebel-held territory without Kiev's consent. Ukraine has offered assistance of its own. But aid, some residents said this week, is not as critical as peace.

'People are able to survive even without electricity and water,' Sologub said as she lay bandaged in a hospital in this government-held village eight miles from Luhansk, a Ukrainian city close to the Russian border that has seen some of the worst combat of the four-month conflict. 'But you can't prepare yourself for bombing.'

Luhansk has been without electricity or water for 20 days, city officials said. But Sologub and her husband were determined to tough it out in the house they built there with their own hands. The rocket attack fractured one of Sologub's legs and severely wounded a foot. Her husband suffered a spinal injury.

The fighting is fueling a growing refugee problem as Luhansk, a city of 425,000 people before the conflict, empties out and residents of Donetsk, about 90 miles to the southwest, flee the hostilities there. The United Nations estimated that at least 190,000 residents of eastern Ukraine had fled to other parts of the country, and it reported that 197,000 had fled to Russia, based on figures provided by the Russian government. An additional 28,000 were believed to have taken refuge in other countries.

More than 2,000 people have died since fighting started in April, the United Nations said. Many of the casualties have occurred in recent weeks as the Ukrainian military, pushing into dense urban centers, tried to deal a final blow to rebels who have been forced to surrender much of the territory they once held.

'We were hoping it wouldn't end this way,' said Iryna Verygina, the pro-Kiev acting governor of the Luhansk region.

Ukrainian President Petro Poroshenko and Russian President Vladimir Putin plan to meet in Minsk, Belarus, on Tuesday, along with their French and German counterparts, in what would be their first face-to-face discussions since early June. Ahead of the meeting - which some officials in Kiev hope will be a first step toward a negotiated end to the conflict - Ukrainian forces appear to be trying to advance as far as they can to improve their bargaining position. The civilian death toll has surged in recent days, reflecting the intensified fighting.

At the crumbling red-brick hospital in Shchastya, whose name means 'happiness' in Ukrainian, shelling and rocket attacks in recent days have been so loud and so constant that nurses sometimes close the rickety windows to try to block out the noise.

Doctors, most of whom are volunteers from elsewhere in Ukraine, said they are receiving an adequate, if not bountiful, amount of medical supplies and other aid. But they are short on equipment, their X-ray machines are rudimentary and the three operating rooms are easily overwhelmed on days such as one two weeks ago when 13 injured people came in for treatment.

Even in Luhansk, doctors said, some hospitals continue to function, although the fuel for their generators is running low after almost three weeks without electricity or water from municipal utilities.

Everyone is learning to live with uncertainty.

'We're within range of the rebels' Grad systems,' said surgeon Anton Nosik, referring to Soviet-era multiple-rocket launchers that the two sides use to spray rockets onto each other's positions. 'But we're trying not to think about that.'

In a refugee transit camp in Svatove, a government-held town in the Luhansk region about 50 miles from the fighting, dozens of people fleeing the war arrive every day. Although there are peaceful swimming holes in the lazy river that passes by the tent city, the scars of war are very present. Many refugees were startled by the resemblance of the camps' showers to rocket launchers. Fireworks for a wedding one recent evening set nerves on edge because they sounded much too much like the violence that people had just left behind.

The first thing the camp offers new arrivals is a shot of cognac and a chance to talk to a counselor, camp administrator Sergey Yakukhin said.

After the cognac, he said, 'people sigh, and then they begin to talk.'

Many in the camp said that they stayed in Luhansk as long as they could but that the shelling simply become too intense. When food supplies ran low, they mixed flour with a touch of water and baked unleavened bread, if they had a way to cook with fire. Those people willing to endure long lines and the risk of shelling can still buy certain food staples. But prices have nearly tripled for cooking oil and quintupled for cigarettes.

'We already know when it's dangerous or not. If you hear the whistle of a rocket, then you know you need to lie on the floor or go in the basement,' said Nadya Poselyeva, 52, who fled Luhansk a week ago and who was flying a tiny Ukrainian flag from the corner of her bed frame in the olive-green military tent she is sharing with 19 other refugees.

All the refugees can tell of friends and family who have died or whose homes have been destroyed. One of Poselyeva's neighbors was killed. Another neighbor's house was destroyed by shelling. Another house went up in flames, she said.

Poselyeva was a receptionist at a university dormitory until the building was taken over by rebels. She stopped work about a month ago because it was no longer safe to go out, she said. After the Ukrainian National Guard warned that it could not guarantee the safety of her house, she fled with clothes for three days, expecting to be able to return shortly. That time still has not come.

'We pray every day that it will end soon,' Poselyeva said. 'We're waiting to go home. We don't want to go anywhere else.'