SVYATOHIRSK, Ukraine -- As fighting escalates around the town Debaltseve in eastern Ukraine, a growing wave of civilians are fleeing their homes, taking the risk of being struck by stray projectiles on their way, and often leaving family members behind.

Prime Minister Arseniy Yatsenyuk said that around 1,000 of Debaltseve's residents have been evacuated in the past days. Many end up at a government-owned holiday camp in the resort town of Svyatohirsk, where the sound of artillery fire is replaced with an uneasy quiet.

"With every slam of the door or whistle, we are reminded of the explosions and everything that happened. But we are getting used to the quiet, which is an unusual feeling," said Ira Akhmutova, 15, who left Debaltseve together with her mother and the few things they could carry.

"My dad and my grandmother are still in Debaltseve. Telephone connections are very poor and I am very worried about them," Akhmutova said.

Fighting has been most intense in the last week around the government-held town, a strategically valuable railway hub that has been almost entirely encircled by rebel forces. Only one road remains open for escape, and that has been targeted by artillery fire.

Ukraine's government said Sunday that 13 of its troops were killed and another 20 wounded in a day of fighting across the east.

Among those who left their homes to go to Svyatohirsk is Galina Maksimenko, 63, and one of her granddaughters.

After one episode of heavy shelling, she recalls pleading with her late son's wife to take her two daughters away from Debaltseve on a government bus for evacuees. The daughter-in-law refused, saying she wanted to remain near her husband's grave.

"I begged her, said to her: 'You have to save the living. You cannot bring Andrei back. Escape with your children,"' Maksimenko said.

And still, the daughter-in-law refused to budge.

"So my husband grabbed my coat and that of one of my granddaughters and locked us out in the street. And then he shouted: 'Save this one. If they refuse to be saved, at least try save one of them," Maksimenko said.

Busses are being dispatched daily to Debaltseve by Ukrainian authorities to carry out as many civilians as possible.

Vasily Stayetsky, deputy chairman of Ukraine state emergency service, told The Associated Press that a projectile crashed Sunday by the town hall, which now serves as a mustering point for those wishing to leave.

"Six people were wounded -- Three were civilians, one was a soldier, and another two were representatives of the state emergency services," Stayetsky said.

Debaltseve has been without power, water, household gas and heating for more than 10 days. Only the relatively mild weather has lightened the extreme discomfort. Mobile phone signals waver between sporadic and nonexistent.

In a Svyatohirsk camp recreation room, one six-year old boy, Sergei, filled in a coloring book and casually told of how a shell fell by a shop in Debaltseve. He said he couldn't tell if it was a Grad or an Uragan rocket.

Prospects for a settlement between the warring sides looked dimmer than ever after negotiations in the Belarusian capital, Minsk, collapsed amid acrimony Saturday.

Ukraine's envoy at the talks, former President Leonid Kuchma, told Interfax-Ukraine news agency that rebel representatives threatened to renew full-scale hostilities along the entire line of contact between the opposing forces. Kuchma said separatists also demanded to redraw a division line agreed by government and rebel forces in September.

In statements following the talks, rebel officials did not address any specific demands, but accused Ukraine of acting in bad faith and pursuing offensive manoeuvrs against their forces and civilians under their jurisdiction. In Donetsk, the main rebel-held city, three civilians were killed and four wounded in shelling, the city administration said.

French President Francois Hollande and German Chancellor Angela Merkel spoke by telephone with Ukrainian President Petro Poroshenko on Sunday, a day after a similar call with Russian President Vladimir Putin. Merkel's office said the German, French and Ukrainian leaders voiced disappointment at the failure of Saturday's talks and called on Russia to use its influence with the separatists to resume the negotiations.

The conflict in east Ukraine has claimed more than 5,100 lives and displaced more than 900,000 people since it began in April, according to U.N. estimates.

In the capital, Kyiv, about 60 Debaltseve residents arrived Sunday to take part in a protest outside the Russian Embassy. An adjacent garden was turned into a symbolic cemetery, with wooden crosses erected in memory of the 30 civilians killed by shelling in the southeastern city of Mariupol in late January.

Plaques on the crosses said they were "killed by Russian occupiers."

"Russia is conducting an undeclared war in Ukraine," said Yevgeny Chebotarev, who met people arriving by train from Debaltseve and was helping them find shelter. "Today it is obvious that behind the DNR and LNR (the Donetsk and Luhansk self-proclaimed republics) stand Russian troops and Russian weapons, whose victims are Ukrainian civilians."

Russia denies sending arms and troops to the rebels, who claim to rely solely on military equipment poached from the Ukrainian army. But the separatist forces have deployed vast quantities of powerful weapons, much of which military experts say are not even in Ukraine's arsenal.