Nadya Volkova, 24, is comforted by her mother-in-law, Galina Nikolaevna, as she grieves over the body of her mother, Katya Volkova, 60, who was killed by shelling at 7:30 a.m. Wednesday as she walked to the store in Avdiivka, Ukraine. (Brendan Hoffman/Getty Images)

Russian-backed separatists kept up a ­rocket and artillery attack on this frigid city Wednesday, in a surge in violence that could pose an early and difficult foreign policy ­challenge to the new Trump ­administration.

A planned evacuation of ­Avdiivka, organized by the ­Ukrainian government, found few takers Wednesday. Only 145 ­residents chose to board buses that would take them away from the fighting; 88 were children.

Sporadic shelling of Avdiivka, on the front line between separatists and regular Ukrainian forces, had intensified early this week, shortly after President Trump and Russian President Vladi­mir Putin had their first phone conversation. The sudden eruption in the long-running conflict in eastern Ukraine threatens to put Trump, who has said he wants better relations with Moscow, on the spot.

Analysts say both Putin and Ukrainian President Petro ­Poroshenko appear to be trying to exploit the intensification of the fighting as a means of influencing the new U.S. administration: Putin could be daring Washington to do something about it; Poroshenko can play up Ukraine’s image as the aggrieved nation.

Small-arms fire and heavier detonations were audible Wednesday throughout the city center. The barrage was ­indiscriminate; on the outskirts of town, Katya Volkova, 60, was killed by shrapnel from a Grad rocket at 7:30 a.m. as she was out for a walk; her distraught ­daughter Nadya was kneeling over the body and weeping.

Local residents queue to receive food and humanitarian aid in Avdiivka, Ukraine, Feb. 1, 2017. (Evgeniy Maloletka/AP)

At the evacuation point, Ania Bohatysh, a 69-year-old pensioner, waved goodbye to her daughter and 17-month-old grandson. “It’s much stronger shelling than it was before, so that’s why I wanted them to leave,” she said. “And now we don’t even have water or heat. It’s simply impossible to sleep anymore because of the shelling.”

But Bohatysh stayed. Avdiivka is her home, she said, and she would rather die here than try to start life over again elsewhere.

Six Ukrainian soldiers have been killed here since Sunday, and 48 have been wounded, while ­unconfirmed reports indicated that the separatists suffered heavy losses. The number of civilian casualties is not clear.

The 20,000 people who remain here, out of a prewar population of 35,000, are without heat and ­water after heavy shelling took out electricity lines and wreaked ­havoc on the city’s Soviet-era coke plant. It is the largest coke producer in Europe and critical to Ukraine’s steel industry.

The plant is working at 20 percent capacity now, according to plant director Musa Magomedov, who said that the town is on the precipice of a humanitarian disaster if the fighting continues.

For the first time since last summer, videos on social media purported to show protracted use of MLRS Grad rockets. The Grad, an imprecise and indiscriminate weapon, was banned under the Minsk II peace agreement, signed nearly two years ago. That agreement also prohibits the use of tanks and heavy artillery. However, according to the Organization for Security and Cooperation in Europe, and reports from soldiers, all of these weapons were back in action over the past few days.

Alex Kokcharov, an analyst at IHS Jane’s, said he believes that the escalation could be a show of force by Russia.

Tanks are seen in the government-held industrial town of Avdiyivka, Ukraine. (Gleb Garanich/Reuters)

“Russia is willing to use the controlled escalation in Donbas to demonstrate its control of the ­conflict to the new U.S. ­administration,” Kokcharov said. “This is likely to be part of the wider ­Russian strategy of foreign and military assertiveness.”

However, the surge also seems to have some political benefit for the administration in Kiev, bringing attention back to a seemingly forgotten conflict. In an unusual step, the bodies of soldiers killed in the latest battles were included in a procession Monday morning in Kiev, on the site of the country’s 2014 revolution.

Trump’s election sent shock waves across Ukraine because of his stated willingness to cut a deal with Russia that could give Moscow a free hand in the region, spelling disaster for Kiev. The administration in Kiev is adamant that discussions of lifting sanctions are entirely premature.

Both sides hope to capi­tal­ize on the fighting, said Alexander Clarkson, a lecturer in European studies at Kings College in London. “My suspicion is that the Ukrainian army and government are not averse to playing up the impact of Russian shelling and general military activity. Poroshenko can now turn around and point to current developments to argue that any removal of sanctions is betrayal against an aggressor.”

At the same time, he said, “Putin’s trap is to dare Trump to do anything about attacks in Donbas after Trump has made such a big deal over partnering with Russia.”

Read more:

An outburst of violence in Ukraine may be Trump’s first test with Putin

Trump says it is ‘very early’ to discuss lifting sanctions on Russia

As Trump seeks warmer ties with Russia, U.S. sends troops to Eastern Europe

Today’s coverage from Post correspondents around the world

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