Anzhelika Sharonova and her 86-year-old mother held out in their battered eastern Ukrainian town for as long as they could before finally fleeing this week with just a few bags between them.

Russian forces are steadily advancing north and south of Toretsk as they press on multiple parts of the eastern front, threatening to eventually envelop the former coal-mining town and others around it.

"There's not a single window left on the fifth floor," said Sharonova, 57, huddled inside a minivan driven by members of East SOS, a relief group helping evacuate civilians.

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"Bombs are falling near our building."

Toretsk has been on the front line of the war with Moscow-backed separatists since 2014, but the recent surge in fighting and a lack of basic services have made life virtually unlivable for Sharonova and her mother Valentyna, the two women said.

They had mostly depended on deliveries of humanitarian aid to the hollowed-out town, where few stores remained open, and the nearest hospital was at least 20 km away.

Buildings on their street were pockmarked and metal cables lay splayed near their entrance. Elsewhere, dogs roamed the streets under the rumble of artillery and a long line of residents snaked from an ATM machine.

In one nearby village, said Valentyna, there had been a "missile (attack) on every house". A day before the two were evacuated, a Russian airstrike had hit a local police station, authorities said.

Less than 12,000 people remain in the greater Toretsk area out of a pre-invasion population of at least 66,000, regional police said.

"With each day, it's more dangerous for people to remain in place, in their homes," said Vladyslav Arseniy, an East SOS rescuer.

Sharonova and her mother are among the two dozen or so people evacuated each week by East SOS, which roves the war-scarred Donetsk region on a near-daily basis responding to calls.

Reuters accompanied the group on a recent mission as it collected elderly and infirm residents from their homes and local hospitals, mostly from cities like Kostiantynivka which are further from the front line.

Two bed-ridden women were laid out across the back of the minivan, and the others packed into the back seat.

Those left in Toretsk, where fields outside the city are marked by both fresh and decade-old trenches, are determined to stay until their homes are completely destroyed, Arseniy said.

Sharonova and her mother, who had endured two wartime winters in their apartment, said they were headed for a larger city in central Ukraine and do not expect to return.

East SOS member Oleksandr Stasenko, speaking outside the train onto which he helped load the several residents the team evacuated that day, said it was difficult seeing frightened people.

"Emotions break through sometimes and you tear up," he said. "But you pull yourself together and help people."