Galina Karpuhina and her two youngest sons are safe now, far away from the rooftop sniper near the yard where the boys played, the schoolhouse pockmarked with bullet holes and the bedroom floor where she made her bed to avoid crossfire coming through the window.

Last week, Karpuhina took the boys from their home near the eastern border at the insistence of her husband, who stayed behind with their oldest son. She packed clothes for the summer, rode 15 hours on the train to Kiev and went by minibus to an abandoned Soviet-era sanitarium she heard about from her church. There, she joined about 80 other Ukrainians fleeing the fighting, with more arriving every day bearing heavy suitcases and heavy hearts.

“I want to return home, but I don’t know when it will be possible,” said Karpuhina, 45, as the sound of birds chirping wafted through windows left open to air out the stale, musty smell of disuse that permeates every room and hallway. “I don’t know if I will even have a house left standing.”

A humanitarian crisis is in the making in Ukraine as tens of thousands of civilians clamor to escape two months of violence in the east.

Ukraine’s new president, Petro Poroshenko, announced this week that the government will create safe-passage corridors for fleeing civilians and provide them public assistance.

But for many, flight only adds a new set of problems. The crisis has developed so fast that the government has organized nothing to assist evacuees. The help is all private, including ­from churches, foundations, activists and ordinary citizens who are converting summer camps and hostels around the country into makeshift shelters.

No one knows how many people have already left, as many find refuge with friends and family elsewhere in Ukraine or across the border in Russia. But the number only climbs as people jump in cars, ­buses and trains to scramble out of the line of fire. Although extra trains have been added, passengers often have to wait days to get seats, and scalpers are asking double the face value for a train ticket.

“They tell us they feel they need to move now, because the next day might be worse,” said Anatoly Zabolotny, director of the Rinat Akhmetov Foundation for the Development of Ukraine, a private foundation funded by a billionaire that has found shelter for more than 1,400 evacuees.

Some charities are overwhelmed by the demand.

“Today, I have more than 75 people here,” said Father Nicolay Ilnytsky, a Ukrainian Orthodox priest who is housing evacuees in a summer retreat normally used by orphans and unwed mothers just outside of the Ukrainian capital, Kiev. “Tomorrow, I’ll have 80 or 85. I just got a call asking me if I could take 23 more people. The government does nothing.’’

Many more residents have stayed than have left, despite the danger. Some remain of their own volition, unwilling to abandon their property and jobs. Others are trapped by fighting outside their doors, making escape nearly impossible.

Olga Turura spent three nights cowering under the dining room table with her 5-year-old son, Miroslav, in Slovyansk, the scene of some of the most intense fighting. Their home is situated between two checkpoints, one manned by Ukrainian troops and one by separatist rebels who sometimes shot at each other down the street outside her front door. The fighting has knocked out power and water, so, without an Internet connection or television, the only way she could tell it was time to leave was by the sound of approaching mortar shells.

Last week, she got into the wheelchair she uses because of a spinal disease, put her son in the back seat of her car and her mother in the front seat, and drove through rutted fields to detour around major checkpoints. Her husband, who works as a janitor, stayed behind, afraid that rebels who have established an autonomous zone near the city of Donetsk would not let him pass.

“It’s hard for the men to get out,” said Turura, 30. “The Donetsk People’s Republic say women and children can go. But they pull men off the buses and say they should stay to protect Slovyansk.”

She has no money. Her bank has blocked the credit cards of all their customers, and she has no friends or family outside Slovyansk. Her sole focus was on getting out. Then she heard about the shelter taking in evacuees in the sanitarium near a small town about 90 miles from Kiev.

Accommodations are spartan, although they hint of long-lost grandeur and shame. The sanitarium was built in 1930 and still has spigots that once dispensed mineral water to vacationing Soviet workers. A historical display in the lobby shows photographs taken in the 1940s when it was a concentration camp for prisoners of war. As Ukrainians began fleeing the east, activists who organized after protests that ousted the previous government suggested to town officials that the sanitarium reopen for evacuees.

They spent a couple of weeks airing out the rooms and sweeping away the dust and accepted the first family from the east two weeks ago, said Vasiliy Dikarev, the facility manager. Most of the 80 displaced people staying there now are women and children. The volunteers have been asked to take up to 200 children for the summer, suggesting few expect the conflict will end anytime soon.

The only ground rule for people seeking shelter is a prohibition on talking politics.

“We are all people of Ukraine,’’ Dikarev said. “They came here from all over because of problems caused by politics. Their minds need a rest.”

Townspeople drop by frequently, driving up the road to the sanitarium through a piney forest teeming with pesky mosquitoes. Many bring newly picked strawberries, milk fresh from cows and boxes of apples. Others drop off used clothes, paper goods and toiletries that are laid out in a corner of the lobby for anyone in need. One local man gives dance lessons. Some come with car trunks stuffed with toys, coloring books and board games for children who play in a freshly painted room, seemingly oblivious to the circumstances that brought them there.

But even the sound of children’s laughter cannot ease the sense of loss and uncertainty that hangs over the sanitarium.

Alla Gopchenko, 46, arrived last Sunday after fleeing Kramatorsk, afraid to stay because her husband, a participant in pro-Ukrainian rallies, had received death threats from pro-Russian separatists. Since they arrived, her 12-year-old daughter has been waking up with nightmares, caused by both her memories of the fighting and her anger at leaving friends behind.

Gopchenko said she is most worried about her parents, who have refused to abandon their home in Slovyansk. Military jets and helicopters fly over her parents’ neighborhood with regularity, and there is shooting, but she said her father promised to care for properties on behalf of neighbors who fled.

“I’ve had no contact with them since I got there,” she said, taking a break from laying out plates of cookies in the cafeteria. “There’s no electricity, so they can’t charge the phone. I keep trying to call them. I don’t know if they’re alive or dead.”

With their futures uncertain, some evacuees have started steeling themselves for the possibility it will be months before they can return.

“I’m not ready to even consider that we may not ever go home again,” said Olga Frolova, 48, a former elections official in Donetsk . “But I'm afraid we might be here for a very long time.”