Ukraine says that its forces have retreated from Soledar after an intense battle.

Ukrainian forces have retreated from the small town of Soledar following weeks of bitter fighting, a military spokesman said on Wednesday, acknowledging a military gain for Russian forces that brings them closer to encircling and possibly capturing the strategic eastern city of Bakhmut.

Col. Sergei Cherevaty, the spokesman for Ukraine’s eastern military command, said that the retreat from Soledar was ordered “to preserve our personnel.”

“Russian forces spent colossal resources in lives and equipment in the effort to take Soledar while Ukraine was able to preserve its forces and prevent encirclement,” he said in an interview.

Soledar, which had a prewar population of around 10,000 people, is six miles northeast of Bakhmut, a city in the eastern part of Ukraine known as Donbas. President Vladimir V. Putin of Russia has sought to fully capture Donbas, which includes two regions — Donetsk and Luhansk. Russian forces have since last summer both shelled Bakhmut and fought for the towns surrounding it, aiming to secure high ground from which to position artillery and also to cut off roads used by Ukraine to reinforce its troops defending the city.

Pavlo Kyrylenko, the head of the Ukrainian military administration in Donetsk, which includes Soledar, said on Tuesday that Russian forces had shelled a string of towns in the region including Paraskoviivka, which is just west of Soledar. One person died in that attack, he said.

Moscow has held significant territory in Donbas since 2014, including two regional capitals. But since seizing two key cities in Luhansk last summer, Russia’s military advances in Donbas have been slow. Both Russian and Ukrainian forces have sustained heavy casualties in intense shelling and trench warfare. In recent weeks, soldiers also have had to endure bitter cold and mud.

The capture of Soledar marks a victory for the Kremlin but also for Yevgeny Prigozhin, the founder of the Wagner private military company, which has spearheaded much of Russia’s fighting around Bakhmut. Mr. Prighozin, a close associate of Mr. Putin, has billed the battle for Bakhmut as a measure of the effectiveness of his fighting force.

Wagner said earlier this month that Soledar had fallen, and military experts have said since last week that Ukraine appeared to have retreated. Wagner also said last week that it had captured the village of Klishchiivka, a few miles south of Bakhmut, in a further sign of its progress toward encircling the city. There was no comment from the Ukrainian military about that claim.

Russian forces “are already increasing pressure” in the direction of Bakhmut, President Volodymyr Zelensky of Ukraine said in a speech late on Tuesday, adding: “And they want to increase pressure on a larger scale.”