The prolonged and bloody battle for Bakhmut has destroyed more than half of the city in eastern Ukraine, a local official said on Thursday.

Pavlo Kyrylenko, the head of the Ukrainian military administration for the Donetsk region, which includes Bakhmut, said that Ukrainian troops are holding off Russian forces but that the defense of the city has come at a cost amid “constant shelling.”

“The city itself suffers from this,” Mr. Kyrylenko said on Ukrainian television. “It is destroyed by more than 60 percent.” Two people were killed there by Russian artillery fire the previous day, he added. The claims could not be independently verified.

Russia has continued to press an offensive aimed at capturing Bakhmut, after suffering a string of setbacks elsewhere in Ukraine in recent months. The city remains one of the Russian military’s main targets, Ukraine’s deputy minister of defense, Hanna Malyar, said on Thursday.

As the battle for Bakhmut has turned into one of the bloodiest campaigns of the war, and losses for both sides have mounted, Ukraine’s defense of the ravaged city has taken on a symbolism that outstrips its military significance, with “Hold Bakhmut” emerging as a rallying cry for the nation.

President Volodymyr Zelensky of Ukraine, who made a daring visit to the city in December, again expressed gratitude in his overnight address for the troops defending it, calling them “warriors.”

Amid the relentless sounds of outgoing and incoming fire, at least 90 percent of the city’s prewar population of 73,000 people have fled.

Donetsk is one of four Ukrainian regions the Kremlin illegally annexed in September even as its troops were losing ground there. Since then, combat in the region has become a bloody slog, as Ukrainian forces look for places to press their advantage, while Russians build trenches and fortifications along the front lines and try to capture Bakhmut.

The Russian force fighting in Donetsk is partly made up of fighters from the Wagner Group, a private military contracting company, and includes convicts who have been promised pardons in exchange for fighting for Moscow in Ukraine. Trench warfare has swayed back and forth over outlying districts of Bakhmut and nearby villages, with advances and retreats on both sides often measured in the hundreds of yards.