But the military’s campaign against the rebels has increased the likelihood of civilian casualties given how deeply the rebels have embedded into the civilian population.

As Ukrainian troops inched toward Donetsk and Luhansk in recent weeks, two regional capitals with a combined population of 1.5 million, residents feared the worst, looking to what happened in Slovyansk, a small city to the north that the military took by pounding rebel positions and flattening the neighborhoods where the rebels were.

Those fears were soon realized. One of the main rebel bases in Luhansk is in a military recruitment office next to the main bus station, and it drew intense shelling, leaving power lines scattered like string over the shrapnel-torn pavement.

And in Donetsk, where Ukrainian troops have pressed forward from the north and west for weeks, the Marinka, Petrovsky and Kuibyshevsky neighborhoods have come under heavy rocket fire. The barrages against all three areas, according to Human Rights Watch, originated from positions held by the Ukrainian military. Mr. Seleznyov said he could not comment on specific events.

On July 21 in Kuibyshevsky, in a leafy area near a dental office and a library, Sergei Yakshin, 41, the man with the alarm business, was walking to his car. He never made it. A rocket exploded nearby, killing him and another man instantly. A short walk away, a different rocket hit Valentina A. Surmai, a 72-year-old pensioner who worked at a local grocery store to support her blind husband. The cook, Alla A. Vasyutina, 60, bled to death in her kitchen after a piece of shrapnel penetrated the wall of her house.

“She wanted to make us soup,” said Ms. Surmai’s son, Sergei, standing in his underwear, his eyes red. “I told her, ‘Mom, don’t go out,’ ” he said. He barely recognized her body in the morgue. Half her face and her left side were gone.

Her death enraged Mr. Surmai. “If they give me a gun, I’m ready to go fight,” he said. “After this, it’s either us, or them. There’s no choice now. We have to go to the end.”